Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization

Physics Reports

Volumn 660, Issue , 2016, Pages 1-94

  Boccaletti, S ^a,b,c   Almendral, J A ^d,e   Guan, S ^a   Leyva, I ^d,e   Liu, Z ^a   Sendina Nadal I ^d,e   Wang, Z ^f   Zou, Y ^a  

^a EAST CHINA NORMAL UNIVERSITY   (China)

^b CNR   (Italy)

^c Italian Embassy   (Israel)

^d UNIVERSIDAD REY JUAN CARLOS   (Spain)

^e UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^f QINGDAO UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85003890196     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physrep.2016.10.004     Document Type: Review

References (449)

1. [1] Jaeger, G., The Ehrenfest classification of phase transitions: introduction and evolution. Arch. Hist. Exact Sci. 53:1 (1998), 51–81, 10.1007/s004070050021.
2. [2] Stauffer, D., Aharony, A., Introduction to Percolation Theory. 1992, Taylor & Francis.
3. [3] Bollobás, B., Riordan, O., Percolation. 2006, Cambridge University Press, Cambridge, New York, Melbourne.
4. [4] Blekhman, I., Synchronization in Science and Technology. 1988, American Society of Mechanical Engineers.
5. [5] Boccaletti, S., Kurths, J., Osipov, G., Valladares, D., Zhou, C., The synchronization of chaotic systems. Phys. Rep. 366:1–2 (2002), 1–101, 10.1016/S0370-1573(02)00137-0.
6. [6] Strogatz, S., Sync: The Emerging Science of Spontaneous Order. 2003, Hyperion.
7. [7] Boccaletti, S., The Synchronized Dynamics of Complex Systems. 2008, Elsevier.
8. [8] Pikovsky, A., Rosenblum, M., Kurths, J., Synchronization: A Universal Concept in Nonlinear Sciences. 2001, Cambridge University Press.
9. [9] Achlioptas, D., D'Souza, R.M., Spencer, J., Explosive percolation in random networks. Science 323:5920 (2009), 1453–1455, 10.1126/science.1167782.
10. [10] Cho, Y.S., Kahng, B., Discontinuous percolation transitions in real physical systems. Phys. Rev. E, 84, 2011, 050102, 10.1103/PhysRevE.84.050102.
11. [11] da Costa, R.A., Dorogovtsev, S.N., Goltsev, A.V., Mendes, J.F.F., Explosive percolation transition is actually continuous. Phys. Rev. Lett., 105, 2010, 255701, 10.1103/PhysRevLett.105.255701.
12. [12] Grassberger, P., Christensen, C., Bizhani, G., Son, S.-W., Paczuski, M., Explosive percolation is continuous, but with unusual finite size behavior. Phys. Rev. Lett., 106, 2011, 225701, 10.1103/PhysRevLett.106.225701.
13. [13] Riordan, O., Warnke, L., Explosive percolation is continuous. Science 333:6040 (2011), 322–324, 10.1126/science.1206241.
14. [14] Pazó, D., Thermodynamic limit of the first-order phase transition in the Kuramoto model. Phys. Rev. E, 72(4), 2005, 046211, 10.1103/PhysRevE.72.046211.
15. [15] Gómez-Gardeñes, J., Gómez, S., Arenas, A., Moreno, Y., Explosive synchronization transitions in scale-free networks. Phys. Rev. Lett. 106:12 (2011), 1–4, 10.1103/PhysRevLett.106.128701.
16. [16] Leyva, I., Sevilla-Escoboza, R., Buldú, J.M., Sendiña-Nadal, I., Gómez-Gardeñes, J., Arenas, A., Moreno, Y., Gómez, S., Jaimes-Reátegui, R., Boccaletti, S., Explosive first-order transition to synchrony in networked chaotic oscillators. Phys. Rev. Lett., 108, 2012, 168702, 10.1103/PhysRevLett.108.168702.
17. [17] Leyva, I., Navas, A., Sendiña-Nadal, I., Almendral, J.A., Buldú, J.M., Zanin, M., Papo, D., Boccaletti, S., Explosive transitions to synchronization in networks of phase oscillators. Sci. Rep., 3, 2013, 1281, 10.1038/srep01281.
18. [18] Leyva, I., Sendiña-Nadal, I., Almendral, J.A., Navas, A., Olmi, S., Boccaletti, S., Explosive synchronization in weighted complex networks. Phys. Rev. E, 88(4), 2013, 042808, 10.1103/PhysRevE.88.042808.
19. [19] Zhang, X., Zou, Y., Boccaletti, S., Liu, Z., Explosive synchronization as a process of explosive percolation in dynamical phase space. Sci. Rep., 4, 2014, 5200, 10.1038/srep05200.
20. [20] Zou, Y., Pereira, T., Small, M., Liu, Z., Kurths, J., Basin of attraction determines hysteresis in explosive synchronization. Phys. Rev. Lett., 112(11), 2014, 114102, 10.1103/PhysRevLett.112.114102.
21. [21] Zhang, X., Boccaletti, S., Guan, S., Liu, Z., Explosive synchronization in adaptive and multilayer networks. Phys. Rev. Lett., 114(3), 2015, 038701, 10.1103/PhysRevLett.114.038701.
22. [22] Sendiña-Nadal, I., Leyva, I., Navas, A., Villacorta-Atienza, J.A., Almendral, J.A., Wang, Z., Boccaletti, S., Effects of degree correlations on the explosive synchronization of scale-free networks. Phys. Rev. E, 91(3), 2015, 032811, 10.1103/PhysRevE.91.032811.
23. [23] Kuramoto, Y., Chemical Oscillations, Waves, and Turbulence. 1984, Springer-Verlag, 10.1007/978-3-642-69689-3.
24. [24] Araújo, N., Grassberger, P., Kahng, B., Schrenk, K., Ziff, R., Recent advances and open challenges in percolation. Eur. Phys. J. Spec. Top. 223:11 (2014), 2307–2321, 10.1140/epjst/e2014-02266-y.
25. [25] Bastas, N., Giazitzidis, P., Maragakis, M., Kosmidis, K., Explosive percolation: Unusual transitions of a simple model. Physica A 407 (2014), 54–65, 10.1016/j.physa.2014.03.085.
26. [26] Saberi, A.A., Recent advances in percolation theory and its applications. Rep. 578 (2015), 1–32, 10.1016/j.physrep.2015.03.003.
27. [27] D'Souza, R.M., Nagler, J., Anomalous critical and supercritical phenomena in explosive percolation. Nat. Phys. 11 (2015), 531–538, 10.1038/NPHYS3378.
28. [28] Adler, J., Bootstrap percolation. Physica A, 453, 1991, 171, 10.1016/0378-4371(91)90295-N.
29. [29] Holroyd, E.A., Sharp metastability threshold for two-dimensional bootstrap percolation. Probab. Theory Related Fields 125:2 (2003), 195–224, 10.1007/s00440-002-0239-x.
30. [30] Chalupa, J., Leath, P.L., Reich, G.R., Bootstrap percolation on a Bethe lattice. J. Phys. C: Solid State Phys., 12(1), 1979, L31.
31. [31] Dorogovtsev, S.N., Goltsev, A.V., Mendes, J.F.F., k-core organization of complex networks. Phys. Rev. Lett., 96, 2006, 040601, 10.1103/PhysRevLett.96.040601.
32. [32] Echenique, P., Gómez-Gardeñes, J., Moreno, Y., Dynamics of jamming transitions in complex networks. Europhys. Lett. 71:2 (2005), 325–331, 10.1209/epl/i2005-10080-8.
33. [33] Ziff, R.M., Explosive growth in biased dynamic percolation on two-dimensional regular lattice networks. Phys. Rev. Lett., 103, 2009, 045701, 10.1103/PhysRevLett.103.045701.
34. [34] Radicchi, F., Fortunato, S., Explosive percolation: A numerical analysis. Phys. Rev. E, 81, 2010, 036110, 10.1103/PhysRevE.81.036110.
35. [35] Ziff, R.M., Scaling behavior of explosive percolation on the square lattice. Phys. Rev. E, 82, 2010, 051105, 10.1103/PhysRevE.82.051105.
36. [36] Bastas, N., Kosmidis, K., Argyrakis, P., Explosive site percolation and finite-size hysteresis. Phys. Rev. E, 84, 2011, 066112, 10.1103/PhysRevE.84.066112.
37. [37] Choi, W., Yook, S.-H., Kim, Y., Explosive site percolation with a product rule. Phys. Rev. E, 84, 2011, 10.1103/PhysRevE.84.020102.
38. [38] Angst, S., Dahmen, S.R., Hinrichsen, H., Hucht, A., Magiera, M.P., Explosive ising. J. Stat. Mech., 2012(06), 2012, L06002, 10.1088/1742-5468/2012/06/L06002.
39. [39] Li, J., Östling, M., Corrected finite-size scaling in percolation. Phys. Rev. E, 86, 2012, 040105, 10.1103/PhysRevE.86.040105.
40. [40] Choi, W., Yook, S.-H., Kim, Y., Bond-site duality and nature of the explosive-percolation phase transition on a two-dimensional lattice. Phys. Rev. E, 86, 2012, 051126, 10.1103/PhysRevE.86.051126.
41. [41] Reis, S.D.S., Moreira, A.A., Andrade, J., Nonlocal product rules for percolation. Phys. Rev. E, 85, 2012, 041112, 10.1103/PhysRevE.85.041112.
42. [42] Choi, W., Chae, H., Yook, S.-H., Kim, Y., Dimensional dependence of phase transitions in explosive percolation. Phys. Rev. E, 90, 2014, 022123, 10.1103/PhysRevE.90.022123.
43. [43] Chae, H., Yook, S.-H., Kim, Y., Explosive percolation on the Bethe lattice. Phys. Rev. E, 85, 2012, 051118, 10.1103/PhysRevE.85.051118.
44. [44] Cho, Y.S., Kim, S.-W., Noh, J.D., Kahng, B., Kim, D., Finite-size scaling theory for explosive percolation transitions. Phys. Rev. E, 82, 2010, 042102, 10.1103/PhysRevE.82.042102.
45. [45] Kim, Y., Yun, Y.-k., Yook, S.-H., Explosive percolation in a nanotube-based system. Phys. Rev. E, 82, 2010, 061105, 10.1103/PhysRevE.82.061105.
46. [46] Nagler, J., Levina, A., Timme, M., Impact of single links in competitive percolation. Nat. Phys. 7 (2011), 265–270, 10.1038/NPHYS1860.
47. [47] Cho, Y.S., Kahng, B., Suppression effect on explosive percolation. Phys. Rev. Lett., 107, 2011, 275703, 10.1103/PhysRevLett.107.275703.
48. [48] Cho, Y.S., Kim, J.S., Park, J., Kahng, B., Kim, D., Percolation transitions in scale-free networks under the achlioptas process. Phys. Rev. Lett., 103(1357), 2009, 02, 10.1103/PhysRevLett.103.135702.
49. [49] Radicchi, F., Fortunato, S., Explosive percolation in scale-free networks. Phys. Rev. Lett., 103(16), 2009, 168701, 10.1103/PhysRevLett.103.168701.
50. [50] Rozenfeld, H.D., Gallos, L.K., Makse, H.A., Explosive percolation in the human protein homology network. Eur. Phys. J. B 75 (2010), 305–310, 10.1140/epjb/e2010-00156-8.
51. [51] Squires, S., Sytwu, K., Alcala, D., Antonsen, T.M., Ott, E., Girvan, M., Weakly explosive percolation in directed networks. Phys. Rev. E, 87, 2013, 052127, 10.1103/PhysRevE.87.052127.
52. [52] Friedman, E.J., Landsberg, A.S., Construction and analysis of random networks with explosive percolation. Phys. Rev. Lett., 103, 2009, 255701, 10.1103/PhysRevLett.103.255701.
53. [53] Araújo, N.A.M., Andrade, S., Ziff, R.M., Herrmann, H.J., Tricritical point in explosive percolation. Phys. Rev. Lett., 106, 2011, 095703, 10.1103/PhysRevLett.106.095703.
54. [54] Andrade, J.S., Herrmann, H.J., Moreira, A.A., Oliveira, C.L.N., Transport on exploding percolation clusters. Phys. Rev. E, 83, 2011, 031133, 10.1103/PhysRevE.83.031133.
55. [55] Giazitzidis, P., Argyrakis, P., Generalized achlioptas process for the delay of criticality in the percolation process. Phys. Rev. E, 88, 2013, 024801, 10.1103/PhysRevE.88.024801.
56. [56] Hooyberghs, H., Schaeybroeck, B.V., Criterion for explosive percolation transitions on complex networks. Phys. Rev. E, 83, 2011, 032101, 10.1103/PhysRevE.83.032101.
57. [57] Qian, J.H., Han, D.D., Ma, Y.G., Criticality and continuity of explosive site percolation in random networks. Europhys. Lett., 100(4), 2012, 48006, 10.1209/0295-5075/100/48006.
58. [58] Pan, R.K., Kivelä, M., Saramäki, J., Kaski, K., Kertész, J., Using explosive percolation in analysis of real-world networks. Phys. Rev. E, 83, 2011, 046112, 10.1103/PhysRevE.83.046112.
59. [59] Nagler, J., Tiessen, T., Gutch, H.W., Continuous percolation with discontinuities. Phys. Rev. X, 2, 2012, 031009, 10.1103/PhysRevX.2.031009.
60. [60] Riordan, O., Warnke, L., Achlioptas processes are not always self-averaging. Phys. Rev. E, 86, 2012, 011129, 10.1103/PhysRevE.86.011129.
61. [61] Zhang, X., Hu, X., Kurths, J., Liu, Z., Explosive synchronization in a general complex network. Phys. Rev. E, 88(1), 2013, 010802, 10.1103/PhysRevE.88.010802.
62. [62] D'Souza, R.M., Mitzenmacher, M., Local cluster aggregation models of explosive percolation. Phys. Rev. Lett., 104, 2010, 195702, 10.1103/PhysRevLett.104.195702.
63. [63] Chen, H., He, G., Huang, F., Shen, C., Hou, Z., Explosive synchronization transitions in complex neural networks. Chaos, 23(3), 2013, 033124, 10.1063/1.4818543.
64. [64] da Costa, R.A., Dorogovtsev, S.N., Goltsev, A.V., Mendes, J.F.F., Critical exponents of the explosive percolation transition. Phys. Rev. E, 89, 2014, 042148, 10.1103/PhysRevE.89.042148.
65. [65] da Costa, R.A., Dorogovtsev, S.N., Goltsev, A.V., Mendes, J.F.F., Solution of the explosive percolation quest: scaling functions and critical exponents. Phys. Rev. E, 90, 2014, 022145, 10.1103/PhysRevE.90.022145.
66. [66] da Costa, R.A., Dorogovtsev, S.N., Goltsev, A.V., Mendes, J.F.F., Solution of the explosive percolation quest. II. Infinite-order transition produced by the initial distributions of clusters, Phys. Rev. E, 91, 2015, 032140, 10.1103/PhysRevE.91.032140.
67. [67] da Costa, R.A., Dorogovtsev, S.N., Goltsev, A.V., Mendes, J.F.F., Inverting the achlioptas rule for explosive percolation. Phys. Rev. E, 91, 2015, 042130, 10.1103/PhysRevE.91.042130.
68. [68] Yi, S.D., Jo, W.S., Kim, B.J., Son, S.-W., Percolation properties of growing networks under an achlioptas process. Europhys. Lett., 103(2), 2013, 26004.
69. [69] Chen, W., Cheng, X., Zheng, Z., Chung, N.N., D'Souza, R.M., Nagler, J., Unstable supercritical discontinuous percolation transitions. Phys. Rev. E, 88, 2013, 042152, 10.1103/PhysRevE.88.042152.
70. [70] Chen, W., D'Souza, R.M., Explosive percolation with multiple giant components. Phys. Rev. Lett., 106, 2011, 115701, 10.1103/PhysRevLett.106.115701.
71. [71] Schrenk, K.J., Felder, A., Deflorin, S., Araújo, N.A.M., D'Souza, R.M., Herrmann, H.J., Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition. Phys. Rev. E, 85, 2012, 031103, 10.1103/PhysRevE.85.031103.
72. [72] Zhang, Y., Wei, W., Guo, B., Zhang, R., Zheng, Z., Formation mechanism and size features of multiple giant clusters in generic percolation processes. Phys. Rev. E, 86, 2012, 051103, 10.1103/PhysRevE.86.051103.
73. [73] Chen, W., Zheng, Z., D'Souza, R.M., Deriving an underlying mechanism for discontinuous percolation. Europhys. Lett., 100(6), 2012, 66006, 10.1209/0295-5075/100/66006.
74. [74] Chen, W., Schröder, M., D'Souza, R.M., Sornette, D., Nagler, J., Microtransition cascades to percolation. Phys. Rev. Lett., 112, 2014, 155701, 10.1103/PhysRevLett.112.155701.
75. [75] Waagen, A., D'Souza, R.M., Given enough choice, simple local rules percolate discontinuously. Eur. Phys. J. B 87:12 (2014), 1–10, 10.1140/epjb/e2014-50278-x.
76. [76] Chen, Y., Cao, Z., Wang, S., Hu, G., Self-organized correlations lead to explosive synchronization. Phys. Rev. E, 91(2), 2015, 022810, 10.1103/PhysRevE.91.022810.
77. [77] Moreira, A.A., Oliveira, E.A., Reis, S.D.S., Herrmann, H.J., Andrade, J.S., Hamiltonian approach for explosive percolation. Phys. Rev. E, 81, 2010, 040101, 10.1103/PhysRevE.81.040101.
78. [78] Araújo, N.A.M., Herrmann, H.J., Explosive percolation via control of the largest cluster. Phys. Rev. Lett., 105, 2010, 035701, 10.1103/PhysRevLett.105.035701.
79. [79] Cho, Y.S., Kahng, B., Kim, D., Cluster aggregation model for discontinuous percolation transitions. Phys. Rev. E, 81, 2010, 030103(R), 10.1103/PhysRevE.81.030103.
80. [80] Manna, S.S., Chatterjee, A., A new route to explosive percolation. Physica A 390 (2011), 177–182, 10.1016/j.physa.2010.10.009.
81. [81] Schrenk, K.J., Araújo, N.A.M., Herrmann, H.J., Gaussian model of explosive percolation in three and higher dimensions. Phys. Rev. E, 84, 2011, 041136, 10.1103/PhysRevE.84.041136.
82. [82] Chung, N.N., Chew, L.Y., Lai, C.H., Spectral analysis on explosive percolation. Europhys. Lett., 101(6), 2013, 66003.
83. [83] Cao, L., Schwarz, J.M., Correlated percolation and tricriticality. Phys. Rev. E, 86, 2012, 061131, 10.1103/PhysRevE.86.061131.
84. [84] Fan, J., Liu, M., Li, L., Chen, X., Continuous percolation phase transitions of random networks under a generalized achlioptas process. Phys. Rev. E, 85, 2012, 061110, 10.1103/PhysRevE.85.061110.
85. [85] Cho, Y.S., Kim, Y.W., Kahng, B., Discontinuous percolation in diffusion-limited cluster aggregation. J. Stat. Mech., 2012(10), 2012, P10004, 10.1088/1742-5468/2012/10/P10004.
86. [86] Cho, Y.S., Hwang, S., Herrmann, H.J., Kahng, B., Avoiding a spanning cluster in percolation models. Science 339 (2013), 1185–1187, 10.1126/science.1230813.
87. [87] Ziff, R.M., Getting the jump on explosive percolation. Science 339:6124 (2013), 1159–1160, 10.1126/science.1235032.
88. [88] Cho, Y.S., Kahng, B., Two types of discontinuous percolation transitions in cluster merging processes. Sci. Rep., 5, 2015, 11905, 10.1038/srep11905.
89. [89] Baxter, G.J., Dorogovtsev, S.N., Goltsev, A.V., Mendes, J.F.F., Bootstrap percolation on complex networks. Phys. Rev. E, 82(1), 2010, 11103, 10.1103/PhysRevE.82.011103.
90. [90] Liu, Y.-Y., Csóka, E., Zhou, H., Pósfai, M., Core percolation on complex networks. Phys. Rev. Lett., 109, 2012, 205703, 10.1103/PhysRevLett.109.205703.
91. [91] Zhao, J.-C., Explosive synchronization of complex networks with different chaotic oscillators. Chin. Phys., 22(6), 2013, 060506, 10.1088/1674-1056/22/6/060506.
92. [92] Cellai, D., Lawlor, A., Dawson, K.A., Gleeson, J.P., Critical phenomena in heterogeneous k-core percolation. Phys. Rev. E, 87, 2013, 022134, 10.1103/PhysRevE.87.022134.
93. [93] Parshani, R., Buldyrev, S.V., Havlin, S., Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition. Phys. Rev. Lett., 105, 2010, 048701, 10.1103/PhysRevLett.105.048701.
94. [94] Parshani, R., Buldyrev, S.V., Havlin, S., Critical effect of dependency groups on the function of networks. Proc. Natl. Acad. Sci. 108:3 (2011), 1007–1010, 10.1073/pnas.1008404108.
95. [95] Gao, J., Buldyrev, S.V., Havlin, S., Stanley, H.E., Robustness of a network of networks. Phys. Rev. Lett., 107, 2011, 195701, 10.1103/PhysRevLett.107.195701.
96. [96] Son, S.-W., Grassberger, P., Paczuski, M., Percolation transitions are not always sharpened by making networks interdependent. Phys. Rev. Lett., 107, 2011, 195702, 10.1103/PhysRevLett.107.195702.
97. [97] Gao, J., Buldyrev, S.V., Stanley, H.E., Havlin, S., Networks formed from interdependent networks. Nat. Phys. 8 (2012), 40–48, 10.1038/NPHYS2180.
98. [98] Li, W., Bashan, A., Buldyrev, S.V., Stanley, H.E., Havlin, S., Cascading failures in interdependent lattice networks: the critical role of the length of dependency links. Phys. Rev. Lett., 108, 2012, 228702, 10.1103/PhysRevLett.108.228702.
99. [99] Shekhtman, L.M., Berezin, Y., Danziger, M.M., Havlin, S., Robustness of a network formed of spatially embedded networks. Phys. Rev. E, 90, 2014, 012809, 10.1103/PhysRevE.90.012809.
100. [100] Baxter, G.J., Dorogovtsev, S.N., Goltsev, A.V., Mendes, J.F.F., Avalanche collapse of interdependent networks. Phys. Rev. Lett., 109, 2012, 248701, 10.1103/PhysRevLett.109.248701.
101. [101] Li, M., Jiang, X., Ma, Y., Shen, X., Zheng, Z., Effect of mixing parts of modular networks on explosive synchronization. Europhys. Lett., 104(5), 2013, 58002, 10.1209/0295-5075/104/58002.
102. [102] Panagiotou, K., Spöel, R., Steger, A., Thomas, H., Explosive percolation in Erdös-Rényi-like random graph processes. Electron. Notes Discrete Math. 38 (2011), 699–704, 10.1016/j.endm.2011.10.017.
103. [103] Boettcher, S., Singh, V., Ziff, R.M., Ordinary percolation with discontinuous transitions. Nat. Commun., 3, 2012, 787, 10.1038/ncomms1774.
104. [104] Matsoukas, T., Abrupt percolation in small equilibrated networks. Phys. Rev. E, 91, 2015, 052105, 10.1103/PhysRevE.91.052105.
105. [105] Maksymenko, M., Moessner, R., Shtengel, K., Reversible first-order transition in Pauli percolation. Phys. Rev. E, 91, 2015, 062103, 10.1103/PhysRevE.91.062103.
106. [106] Buldyrev, S.V., Parshani, R., Paul, G., Stanley, H.E., Havlin, S., Catastrophic cascade of failures in interdependent networks. Nature 464 (2010), 1025–1028, 10.1038/nature08932.
107. [107] H.K. Lee, B.J. Kim, H. Park, Continuity of the explosive percolation transition, Phys. Rev. E 84. http://dx.doi.org/10.1103/PhysRevE.84.020101.
108. [108] Spencer, J., Wormald, N., Birth control for giants. Combinatorica 27 (2007), 587–628, 10.1007/s00493-007-2163-2.
109. [109] Riordan, O., Warnke, L., Achlioptas process phase transitions are continuous. Ann. Appl. Probab. 22:4 (2012), 1450–1464, 10.1214/11-AAP798.
110. [110] Bohman, T., Frieze, A., Wormald, N.C., Avoidance of a giant component in half the edge set of a random graph. Random Struct. Algorithms 25:4 (2004), 432–449, 10.1002/rsa.20038.
111. [111] Pittel, B., Spencer, J., Wormald, N.C., Sudden emergence of a giant k-core in a random graph. J. Combin. Theory Ser. B, 111, 1996, 67, 10.1006/jctb.1996.0036.
112. [112] Schwarz, J.M., Liu, A.J., Chayes, L.Q., The onset of jamming as the sudden emergence of an infinite k -core cluster. Europhys. Lett., 73(4), 2006, 560, 10.1209/epl/i2005-10421-7.
113. [113] Oliveira, C.L.N., Araújo, N.A., Andrade, J.S., Herrmann, H.J., Explosive electric breakdown due to conducting-particle deposition on an insulating substrate. Phys. Rev. Lett., 113, 2014, 155701, 10.1103/PhysRevLett.113.155701.
114. [114] Landau, D., Binder, K., A Guide to Monte Carlo Simulations in Statistical Physics. 2015, Cambridge University Press, Cambridge, England, 10.1017/CBO9780511614460.
115. [115] Chaikin, P.M., Lubensky, T.C., Principles of Condensed Matter Physics. 1995, Cambridge University Press, Cambridge, England, 10.1017/CBO9780511813467.
116. [116] Gross, T., D'Lima, C.J.D., Blasius, B., Epidemic dynamics on an adaptive network. Phys. Rev. Lett., 96, 2006, 208701, 10.1103/PhysRevLett.96.208701.
117. [117] Zhang, Y., Wei, W., Guo, B., Zhang, R., Zheng, Z., Criticality and scaling behavior of percolation with multiple giant clusters under an achlioptas process. Phys. Rev. E, 88, 2013, 062103, 10.1103/PhysRevE.88.062103.
118. [118] Chen, W., Zheng, Z., Jiang, X., Souza, R.M.D., Multiple discontinuous percolation transitions on scale-free networks. J. Stat. Mech., 2015, P04011, 10.1088/1742-5468/2015/04/P04011.
119. [119] Bruce, A.D., Wilding, N.B., Scaling fields and universality of the liquid-gas critical point. Phys. Rev. Lett. 68 (1992), 193–196, 10.1103/PhysRevLett.68.193.
120. [120] Privman, V., Finite-size Scaling Theory. Finite Size Scaling and Numerical Simulation of Statistical Systems. 2014, World Scientific, 10.1142/9789814503419_0001.
121. [121] Tian, L., Shi, D.N., The nature of explosive percolation phase transition. Phys. Lett. A 376:4 (2012), 286–289, 10.1016/j.physleta.2011.11.039.
122. [122] Bergé, P., Pomeau, Y., Vidal, C., Order Within Chaos: Towards a Deterministic Approach to Turbulence. 1985, Wiley.
123. [123] Manrubia, S., Mikhailov, A., Zanette, D., Emergence of Dynamical Order: Synchronization Phenomena in Complex Systems. 2004, World Scientific.
124. [124] Letellier, C., Aguirre, L.A., Interplay between synchronization, observability, and dynamics. Phys. Rev. E 82:1 (2010), 1–11, 10.1103/PhysRevE.82.016204.
125. [125] Bianco-Martinez, E., Baptista, M.S., Letellier, C., Symbolic computations of nonlinear observability. Phys. Rev. E, 91(6), 2015, 062912, 10.1103/PhysRevE.91.062912.
126. [126] Sendiña-Nadal, I., Letellier, C., Boccaletti, S., Observability coefficients for predicting the class of synchronizability from the algebraic structure of the local oscillators. Phys. Rev. E, 94, 2016, 042205.
127. [127] Daido, H., Intrinsic fluctuations and a phase transition in a class of large populations of interacting oscillators. J. Stat. Phys. 60:5 (1990), 753–800, 10.1007/BF01025993.
128. [128] Winfree, A.T., Biological rhythms and the behavior of populations of coupled oscillators. J. Theoret. Biol. 16:1 (1967), 15–42, 10.1016/0022-5193(67)90051-3.
129. [129] Valdeolmillos, M., Gomis, a., Sánchez-Andrés, J.V., In vivo synchronous membrane potential oscillations in mouse pancreatic beta-cells: lack of co-ordination between islets. J. Physiol. 493:1 (1996), 9–18, 10.1113/jphysiol.1996.sp021361.
130. [130] Wood, K., Van den Broeck, C., Kawai, R., Lindenberg, K., Continuous and discontinuous phase transitions and partial synchronization in stochastic three-state oscillators. Phys. Rev. E, 76, 2007, 041132, 10.1103/PhysRevE.76.041132.
131. [131] Filatrella, G., Pedersen, N.F., Wiesenfeld, K., Generalized coupling in the Kuramoto model. Phys. Rev. E, 75, 2007, 017201, 10.1103/PhysRevE.75.017201.
132. [132] Tanaka, H.-A., Lichtenberg, A.J., Oishi, S., First order phase transition resulting from finite inertia in coupled oscillator systems. Phys. Rev. Lett. 78:11 (1997), 2104–2107, 10.1103/PhysRevLett.78.2104.
133. [133] Acebrón, J.A., Bonilla, L.L., Spigler, R., Synchronization in populations of globally coupled oscillators with inertial effects. Phys. Rev. E 62 (2000), 3437–3454, 10.1103/PhysRevE.62.3437.
134. [134] Choi, M., Kim, H., Kim, D., Hong, H., Synchronization in a system of globally coupled oscillators with time delay. Phys. Rev. E 61:1 (2000), 371–381, 10.1103/PhysRevE.61.371.
135. [135] Giannuzzi, F., Marinazzo, D., Nardulli, G., Pellicoro, M., Stramaglia, S., Phase diagram of a generalized Winfree model. Phys. Rev. E, 75(5), 2007, 051104, 10.1103/PhysRevE.75.051104.
136. [136] Rosenblum, M., Pikovsky, A., Self-organized quasiperiodicity in oscillator ensembles with global nonlinear coupling. Phys. Rev. Lett., 98(6), 2007, 064101, 10.1103/PhysRevLett.98.064101.
137. [137] Strogatz, S., Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering Advanced Book Program, 1994, Westview Press.
138. [138] Afraimovich, V.S., Verichev, N.N., Rabinovich, M.I., Stochastic synchronization of oscillation in dissipative systems. Radiophys. Quantum Electron. 29:9 (1986), 795–803, 10.1007/BF01034476.
139. [139] Pecora, L.M., Carroll, T.L., Synchronization in chaotic systems. Phys. Rev. Lett. 64 (1990), 821–824, 10.1103/PhysRevLett.64.821.
140. [140] Pecora, L.M., Carroll, T.L., Master stability functions for synchronized coupled systems. Phys. Rev. Lett. 80 (1998), 2109–2112, 10.1103/PhysRevLett.80.2109.
141. [141] Arnol'd, V.I., Small denominators. I. Mapping the circle onto itself. Izv. Ross. Akad. Nauk, Ser. Fiz. 25:1 (1961), 21–86.
142. [142] Rosenblum, M.G., Pikovsky, A.S., Kurths, J., Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 76:11 (1996), 1804–1807, 10.1103/PhysRevLett.76.1804.
143. [143] Zaks, M.A., Park, E.-H., Rosenblum, M.G., Kurths, J., Alternating locking ratios in imperfect phase synchronization. Phys. Rev. Lett. 82 (1999), 4228–4231, 10.1103/PhysRevLett.82.4228.
144. [144] Pujol-Peré, A., Calvo, O., Matías, M.A., Kurths, J., Experimental study of imperfect phase synchronization in the forced Lorenz system. Chaos 13:1 (2003), 319–326, 10.1063/1.1525126.
145. [145] Rosenblum, M., Pikovsky, A., Kurths, J., From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett. 78:22 (1997), 4193–4196, 10.1103/PhysRevLett.78.4193.
146. [146] Voss, H.U., Anticipating chaotic synchronization. Phys. Rev. E 61 (2000), 5115–5119, 10.1103/PhysRevE.61.5115.
147. [147] Voss, H.U., Anticipating chaotic synchronization. Phys. Rev. E, 64, 2001, 039904 Phys. Rev. E, 61, 2000, 5115 (erratum). http://dx.doi.org/10.1103/PhysRevE.64.039904.
148. [148] Heil, T., Fischer, I., Elsässer, W., Mulet, J., Mirasso, C.R., Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers. Phys. Rev. Lett. 86:5 (2001), 795–798, 10.1103/PhysRevLett.86.795.
149. [149] White, J.K., Matus, M., Moloney, J.V., Achronal generalized synchronization in mutually coupled semiconductor lasers. Phys. Rev. E, 65, 2002, 036229, 10.1103/PhysRevE.65.036229.
150. [150] Fischer, I., Vicente, R., Buldú, J.M., Peil, M., Mirasso, C.R., Torrent, M.C., García-Ojalvo, J., Zero-lag long-range synchronization via dynamical relaying. Phys. Rev. Lett., 97, 2006, 123902, 10.1103/PhysRevLett.97.123902.
151. [151] Wagemakers, A., Buldú, J.M., Sanjuan, M.A.F., Experimental demonstration of bidirectional chaotic communication by means of isochronal synchronization. Europhys. Lett., 81(4), 2008, 40005, 10.1209/0295-5075/81/40005.
152. [152] Klein, E., Gross, N., Rosenbluh, M., Kinzel, W., Khaykovich, L., Kanter, I., Stable isochronal synchronization of mutually coupled chaotic lasers. Phys. Rev. E, 73, 2006, 066214, 10.1103/PhysRevE.73.066214.
153. [153] Peil, M., Larger, L., Fischer, I., Versatile and robust chaos synchronization phenomena imposed by delayed shared feedback coupling. Phys. Rev. E, 76, 2007, 045201, 10.1103/PhysRevE.76.045201.
154. [154] Tiana-Alsina, J., Hicke, K., Porte, X., Soriano, M.C., Torrent, M.C., Garcia-Ojalvo, J., Fischer, I., Zero-lag synchronization and bubbling in delay-coupled lasers. Phys. Rev. E, 85, 2012, 026209, 10.1103/PhysRevE.85.026209.
155. [155] Da Silva, I.G., Buldú, J.M., Mirasso, C.R., García-Ojalvo, J., Synchronization by dynamical relaying in electronic circuit arrays. Chaos, 16(4), 2006, 043113, 10.1063/1.2374860.
156. [156] Zhou, B.B., Roy, R., Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillators. Phys. Rev. E, 75, 2007, 026205, 10.1103/PhysRevE.75.026205.
157. [157] Wagemakers, A., Buldú, J.M., Sanjuán, M.A.F., Isochronous synchronization in mutually coupled chaotic circuits. Chaos, 17(2), 2007, 023128, 10.1063/1.2737820.
158. [158] Englert, A., Kinzel, W., Aviad, Y., Butkovski, M., Reidler, I., Zigzag, M., Kanter, I., Rosenbluh, M., Zero lag synchronization of chaotic systems with time delayed couplings. Phys. Rev. Lett., 104, 2010, 114102, 10.1103/PhysRevLett.104.114102.
159. [159] Wu, J.G., Wu, Z.M., Xia, G.Q., Deng, T., Lin, X.D., Tang, X., Feng, G.Y., Isochronous synchronization between chaotic semiconductor lasers over 40-km fiber links. IEEE Photonics Technol. Lett. 23:24 (2011), 1854–1856, 10.1109/LPT.2011.2170212.
160. [160] Vicente, R., Mirasso, C.R., Fischer, I., Simultaneous bidirectional message transmission in a chaos-based communication scheme. Opt. Lett. 32:4 (2007), 403–405, 10.1364/OL.32.000403.
161. [161] Vicente, R., Pipa, G., Fischer, I., Mirasso, C.R., Zero-lag long range synchronization of neurons is enhanced by dynamical relaying. de Sá, J.M., Alexandre, L.A., Duch, W., Mandic, D., (eds.) Artificial Neural Networks, 2007, Springer, Berlin, Heidelberg, 904–913, 10.1007/978-3-540-74690-4_92.
162. [162] Vicente, R., Gollo, L.L., Mirasso, C.R., Fischer, I., Pipa, G., Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays. Proc. Natl. Acad. Sci. 105:44 (2008), 17157–17162, 10.1073/pnas.0809353105.
163. [163] Esfahani, Z.G., Valizadeh, A., Zero-lag synchronization despite inhomogeneities in a relay system. PLoS One, 9(12), 2014, e112688, 10.1371/journal.pone.0112688.
164. [164] Voss, H.U., Dynamic long-term anticipation of chaotic states. Phys. Rev. Lett., 87, 2001, 014102, 10.1103/PhysRevLett.87.014102.
165. [165] Masoller, C., Zanette, D.H., Anticipated synchronization in coupled chaotic maps with delays. Physica A 300:3–4 (2001), 359–366, 10.1016/S0378-4371(01)00362-4.
166. [166] Ciszak, M., Calvo, O., Masoller, C., Mirasso, C.R., Toral, R., Anticipating the response of excitable systems driven by random forcing. Phys. Rev. Lett., 90, 2003, 204102, 10.1103/PhysRevLett.90.204102.
167. [167] Toral, R., Masoller, C., Mirasso, C.R., Ciszak, M., Calvo, O., Characterization of the anticipated synchronization regime in the coupled fitzhugh-nagumo model for neurons. Physica A 325:1–2 (2003), 192–198, 10.1016/S0378-4371(03)00198-5.
168. [168] Ciszak, M., Marino, F., Toral, R., Balle, S., Dynamical mechanism of anticipating synchronization in excitable systems. Phys. Rev. Lett., 93, 2004, 114102, 10.1103/PhysRevLett.93.114102.
169. [169] Matias, F.S., Carelli, P.V., Mirasso, C.R., Copelli, M., Anticipated synchronization in a biologically plausible model of neuronal motifs. Phys. Rev. E, 84, 2011, 021922, 10.1103/PhysRevE.84.021922.
170. [170] Kostur, M., Hänggi, P., Talkner, P., Mateos, J.L., Anticipated synchronization in coupled inertial ratchets with time-delayed feedback: A numerical study. Phys. Rev. E, 72, 2005, 036210, 10.1103/PhysRevE.72.036210.
171. [171] Ciszak, M., Mayol, C., Mirasso, C.R., Toral, R., Anticipated synchronization in coupled complex Ginzburg-Landau systems. Phys. Rev. E, 92, 2015, 032911, 10.1103/PhysRevE.92.032911.
172. [172] Voss, H.U., Real-time anticipation of chaotic states of an electronic circuit. Int. J. Bifurcation Chaos 12:07 (2002), 1619–1625, 10.1142/S0218127402005340.
173. [173] Pethel, S.D., Corron, N.J., Underwood, Q.R., Myneni, K., Information flow in chaos synchronization: Fundamental tradeoffs in precision, delay, and anticipation. Phys. Rev. Lett., 90, 2003, 254101, 10.1103/PhysRevLett.90.254101.
174. [174] Zamora-Munt, J., Mirasso, C.R., Toral, R., Suppression of deterministic and stochastic extreme desynchronization events using anticipated synchronization. Phys. Rev. E, 89, 2014, 012921, 10.1103/PhysRevE.89.012921.
175. [175] Sivaprakasam, S., Shahverdiev, E.M., Spencer, P.S., Shore, K.A., Experimental demonstration of anticipating synchronization in chaotic semiconductor lasers with optical feedback. Phys. Rev. Lett., 87, 2001, 154101, 10.1103/PhysRevLett.87.154101.
176. [176] Buldú, J.M., Vicente, R., Pérez, T., Mirasso, C.R., Torrent, M.C., García-Ojalvo, J., Periodic entrainment of power dropouts in mutually coupled semiconductor lasers. Appl. Phys. Lett. 81:27 (2002), 5105–5107, 10.1063/1.1533837.
177. [177] Ciszak, M., Mirasso, C.R., Toral, R., Calvo, O., Predict-prevent control method for perturbed excitable systems. Phys. Rev. E, 79, 2009, 046203, 10.1103/PhysRevE.79.046203.
178. [178] Rulkov, N.F., Sushchik, M.M., Tsimring, L.S., Abarbanel, H.D.I., Generalized synchronization of chaos in directionally coupled chaotic systems. Phys. Rev. E 51:2 (1995), 980–994, 10.1103/PhysRevE.51.980.
179. [179] Kocarev, L., Parlitz, U., Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. Phys. Rev. Lett. 76:11 (1996), 1816–1819, 10.1103/PhysRevLett.76.1816.
180. [180] Pyragas, K., Weak and strong synchronization of chaos. Phys. Rev. E 54:5 (1996), R4508–R4511, 10.1103/PhysRevE.54.R4508.
181. [181] Abarbanel, H.D.I., Rulkov, N., Sushchik, M., Generalized synchronization of chaos: The auxiliary system approach. Phys. Rev. E 53:5 (1996), 4528–4535, 10.1103/PhysRevE.53.4528.
182. [182] Landsman, A.S., Schwartz, I.B., Complete chaotic synchronization in mutually coupled time-delay systems. Phys. Rev. E, 75(2), 2007, 026201, 10.1103/PhysRevE.75.026201.
183. [183] Moskalenko, O.I., Koronovskii, A.A., Hramov, A.E., Boccaletti, S., Generalized synchronization in mutually coupled oscillators and complex networks. Phys. Rev. E, 86, 2012, 036216, 10.1103/PhysRevE.86.036216.
184. [184] Gutiérrez, R., Sevilla-Escoboza, R., Piedrahita, P., Finke, C., Feudel, U., Buldú, J.M., Huerta-Cuellar, G., Jaimes-Reátegui, R., Moreno, Y., Boccaletti, S., Generalized synchronization in relay systems with instantaneous coupling. Phys. Rev. E, 88, 2013, 052908, 10.1103/PhysRevE.88.052908.
185. [185] Saxena, G., Prasad, A., Ramaswamy, R., Amplitude death: The emergence of stationarity in coupled nonlinear systems. Phys. Rep. 521:5 (2012), 205–228, 10.1016/j.physrep.2012.09.003.
186. [186] Koseska, A., Volkov, E., Kurths, J., Oscillation quenching mechanisms: Amplitude vs. oscillation death. Phys. Rep. 531:4 (2013), 173–199, 10.1016/j.physrep.2013.06.001.
187. [187] Kuramoto, Y., Self-entrainment of a population of coupled non-linear oscillators. International Symposium on Mathematical Problems in Theoretical Physics, 1975, Springer, Berlin, Heidelberg, 420–422, 10.1007/BFb0013365.
188. [188] Winfree, A.T., The Geometry of Biological Time. 1980, Springer, Berlin, 10.1007/978-1-4757-3484-3.
189. [189] Murray, J.D., Mathematical Biology. 1989, Springer, Berlin, 10.1007/b98868.
190. [190] Kapral, R., Showalter, K., (eds.) Chemical Waves and Patterns, 1995, Springer Netherlands, 10.1007/978-94-011-1156-0.
191. [191] Kheowan, O.-U., Mihaliuk, E., Blasius, B., Sendiña-Nadal, I., Showalter, K., Wave mediated synchronization of nonuniform oscillatory media. Phys. Rev. Lett., 98, 2007, 074101, 10.1103/PhysRevLett.98.074101.
192. [192] Leyva, I., Navas, A., Sendiña-Nadal, I., Buldú, J.M., Almendral, J.A., Boccaletti, S., Synchronization waves in geometric networks. Phys. Rev. E, 84, 2011, 065101, 10.1103/PhysRevE.84.065101.
193. [193] Osipov, G.V., Kurths, J., Zhou, C., Synchronization in Oscillatory Networks. 2007, Springer, Berlin, Heidelberg, 103–128, 10.1007/978-3-540-71269-5_5.
194. [194] Kaneko, K., Spatiotemporal intermittency in coupled map lattices. Progr. Theoret. Phys. 74:5 (1985), 1033–1044, 10.1143/PTP.74.1033.
195. [195] Kaneko, K., Theory and Applications of Coupled Map Lattices. 1993, Wiley.
196. [196] Hasler, M., Maistrenko, Y., Popovych, O., Simple example of partial synchronization of chaotic systems. Phys. Rev. E 58:5 (1998), 6843–6846, 10.1103/PhysRevE.58.6843.
197. [197] Heagy, J.F., Carroll, T.L., Pecora, L.M., Synchronous chaos in coupled oscillator systems. Phys. Rev. E 50:3 (1994), 1874–1885, 10.1103/PhysRevE.50.1874.
198. [198] Heagy, J.F., Pecora, L.M., Carroll, T.L., Short wavelength bifurcations and size instabilities in coupled oscillator systems. Phys. Rev. Lett. 74:21 (1995), 4185–4188, 10.1103/PhysRevLett.74.4185.
199. [199] Belykh, V.N., Belykh, I.V., Hasler, M., Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems. Phys. Rev. E 62:5 (2000), 6332–6345, 10.1103/PhysRevE.62.6332.
200. [200] Belykh, V.N., Belykh, I.V., Mosekilde, E., Cluster synchronization modes in an ensemble of coupled chaotic oscillators. Phys. Rev. E, 63(3), 2001, 036216, 10.1103/PhysRevE.63.036216.
201. [201] Cross, M.C., Hohenberg, P.C., Pattern formation outside of equilibrium. Rev. Modern Phys. 65:3 (1993), 851–1112, 10.1103/RevModPhys.65.851.
202. [202] Aranson, I.S., Kramer, L., The world of the complex Ginzburg-Landau equation. Rev. Modern Phys. 74:1 (2002), 99–143, 10.1103/RevModPhys.74.99.
203. [203] Kaneko, K., Globally coupled circle maps. Physica D 54:1–2 (1991), 5–19, 10.1016/0167-2789(91)90103-G.
204. [204] Manrubia, S.C., Mikhailov, A.S., Mutual synchronization and clustering in randomly coupled chaotic dynamical networks. Phys. Rev. E 60:2 (1999), 1579–1589, 10.1103/PhysRevE.60.1579.
205. [205] Popovych, O., Maistrenko, Y., Mosekilde, E., Loss of coherence in a system of globally coupled maps. Phys. Rev. E, 64(2), 2001, 026205, 10.1103/PhysRevE.64.026205.
206. [206] Pikovsky, A., Popovych, O., Maistrenko, Y., Resolving clusters in chaotic ensembles of globally coupled identical oscillators. Phys. Rev. Lett., 87(4), 2001, 044102, 10.1103/PhysRevLett.87.044102.
207. [207] Kocarev, L., Parlitz, U., Synchronizing spatiotemporal chaos in coupled nonlinear oscillators. Phys. Rev. Lett. 77:11 (1996), 2206–2209, 10.1103/PhysRevLett.77.2206.
208. [208] Zanette, D.H., Mikhailov, A.S., Condensation in globally coupled populations of chaotic dynamical systems. Phys. Rev. E 57:1 (1998), 276–281, 10.1103/PhysRevE.57.276.
209. [209] Han, S.K., Kurrer, C., Kuramoto, Y., Dephasing and bursting in coupled neural oscillators. Phys. Rev. Lett. 75:17 (1995), 3190–3193, 10.1103/PhysRevLett.75.3190.
210. [210] Daido, H., Nakanishi, K., Diffusion-induced inhomogeneity in globally coupled oscillators: Swing-by mechanism. Phys. Rev. Lett., 96(5), 2006, 054101, 10.1103/PhysRevLett.96.054101.
211. [211] Yeldesbay, A., Pikovsky, A., Rosenblum, M., Chimeralike states in an ensemble of globally coupled oscillators. Phys. Rev. Lett., 112(14), 2014, 144103, 10.1103/PhysRevLett.112.144103.
212. [212] Mirollo, R.E., Strogatz, S.H., Synchronization of pulse-coupled biological oscillators. SIAM J. Appl. Math. 50:6 (1990), 1645–1662, 10.1137/0150098.
213. [213] van Vreeswijk, C., Partial synchronization in populations of pulse-coupled oscillators. Phys. Rev. E 54:5 (1996), 5522–5537, 10.1103/PhysRevE.54.5522.
214. [214] Mohanty, P.K., Politi, A., A new approach to partial synchronization in globally coupled rotators. J. Phys. A: Math. Gen. 39:26 (2006), L415–L421, 10.1088/0305-4470/39/26/L01.
215. [215] Wang, W., Kiss, I.Z., Hudson, J.L., Experiments on arrays of globally coupled chaotic electrochemical oscillators: Synchronization and clustering. Chaos, 10(1), 2000, 248, 10.1063/1.166470.
216. [216] Pecora, L.M., Synchronization conditions and desynchronizing patterns in coupled limit-cycle and chaotic systems. Phys. Rev. E 58:1 (1998), 347–360, 10.1103/PhysRevE.58.347.
217. [217] Abrams, D.M., Strogatz, S.H., Chimera states for coupled oscillators. Phys. Rev. Lett., 93(17), 2004, 174102, 10.1103/PhysRevLett.93.174102.
218. [218] Battogtokh, D., Kuramoto, Y., Turbulence of nonlocally coupled oscillators in the Benjamin-Feir stable regime. Phys. Rev. E 61:3 (2000), 3227–3229, 10.1103/PhysRevE.61.3227.
219. [219] Omel'chenko, O.E., Maistrenko, Y.L., Tass, P.A., Chimera states: The natural link between coherence and incoherence. Phys. Rev. Lett., 100(4), 2008, 044105, 10.1103/PhysRevLett.100.044105.
220. [220] Abrams, D.M., Mirollo, R., Strogatz, S.H., Wiley, D.A., Solvable model for chimera states of coupled oscillators. Phys. Rev. Lett., 101(8), 2008, 084103, 10.1103/PhysRevLett.101.084103.
221. [221] Bordyugov, G., Pikovsky, A., Rosenblum, M., Self-emerging and turbulent chimeras in oscillator chains. Phys. Rev. E, 82(3), 2010, 035205, 10.1103/PhysRevE.82.035205.
222. [222] Martens, E.A., Laing, C.R., Strogatz, S.H., Solvable model of spiral wave chimeras. Phys. Rev. Lett., 104(4), 2010, 044101, 10.1103/PhysRevLett.104.044101.
223. [223] Omel'chenko, O.E., Wolfrum, M., Maistrenko, Y.L., Chimera states as chaotic spatiotemporal patterns. Phys. Rev. E, 81(6), 2010, 065201, 10.1103/PhysRevE.81.065201.
224. [224] Omelchenko, I., Maistrenko, Y., Hövel, P., Schöll, E., Loss of coherence in dynamical networks: Spatial chaos and chimera states. Phys. Rev. Lett., 106(23), 2011, 234102, 10.1103/PhysRevLett.106.234102.
225. [225] Tinsley, M.R., Nkomo, S., Showalter, K., Chimera and phase-cluster states in populations of coupled chemical oscillators. Nat. Phys. 8:9 (2012), 662–665, 10.1038/nphys2371.
226. [226] Nkomo, S., Tinsley, M.R., Showalter, K., Chimera states in populations of nonlocally coupled chemical oscillators. Phys. Rev. Lett., 110(24), 2013, 244102, 10.1103/PhysRevLett.110.244102.
227. [227] Hagerstrom, A.M., Murphy, T.E., Roy, R., Hövel, P., Omelchenko, I., Schöll, E., Experimental observation of chimeras in coupled-map lattices. Nat. Phys. 8:9 (2012), 658–661, 10.1038/NPHYS2372.
228. [228] Martens, E.A., Thutupalli, S., Fourriere, A., Hallatschek, O., Chimera states in mechanical oscillator networks. Proc. Natl. Acad. Sci. 110:26 (2013), 10563–10567, 10.1073/pnas.1302880110.
229. [229] Laing, C.R., The dynamics of chimera states in heterogeneous Kuramoto networks. Physica D 238:16 (2009), 1569–1588, 10.1016/j.physd.2009.04.012.
230. [230] Laing, C.R., Rajendran, K., Kevrekidis, I.G., Chimeras in random non-complete networks of phase oscillators. Chaos, 22(1), 2012, 013132, 10.1063/1.3694118.
231. [231] Kaneko, K., Clustering, coding, switching, hierarchical ordering, and control in a network of chaotic elements. Physica D 41:2 (1990), 137–172, 10.1016/0167-2789(90)90119-A.
232. [232] Panaggio, M.J., Abrams, D.M., Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators. Nonlinearity 28:3 (2015), R67–R87, 10.1088/0951-7715/28/3/R67.
233. [233] Osipov, G.V., Pikovsky, A.S., Rosenblum, M.G., Kurths, J., Phase synchronization effects in a lattice of nonidentical Rössler oscillators. Phys. Rev. E 55:3 (1997), 2353–2361, 10.1103/PhysRevE.55.2353.
234. [234] Osipov, G.V., Sushchik, M.M., Synchronized clusters and multistability in arrays of oscillators with different natural frequencies. Phys. Rev. E 58:6 (1998), 7198–7207, 10.1103/PhysRevE.58.7198.
235. [235] Pikovsky, A.S., Rosenblum, M.G., Kurths, J., Synchronization in a population of globally coupled chaotic oscillators. Europhys. Lett., 34(3), 1996, 165, 10.1209/epl/i1996-00433-3.
236. [236] Strogatz, S.H., Mirollo, R.E., Collective synchronisation in lattices of nonlinear oscillators with randomness. J. Phys. A 21:13 (1988), L699–L705, 10.1088/0305-4470/21/13/005.
237. [237] Strogatz, S.H., From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D 143:1 (2000), 1–20, 10.1016/S0167-2789(00)00094-4.
238. [238] Acebrón, J.A., Bonilla, L.L., Pérez Vicente, C.J., Ritort, F., Spigler, R., The Kuramoto model: A simple paradigm for synchronization phenomena. Rev. Modern Phys. 77:1 (2005), 137–185, 10.1103/RevModPhys.77.137.
239. [239] Dörfler, F., Bullo, F., Synchronization in complex networks of phase oscillators: A survey. Automatica 50:6 (2014), 1539–1564, 10.1016/j.automatica.2014.04.012.
240. [240] Rodrigues, F.A., Peron, T.K.D., Ji, P., Kurths, J., The Kuramoto model in complex networks. Phys. Rep. 610 (2015), 1–98, 10.1016/j.physrep.2015.10.008.
241. [241] Ott, E., Antonsen, T.M., Low dimensional behavior of large systems of globally coupled oscillators. Chaos, 18(3), 2008, 037113, 10.1063/1.2930766.
242. [242] Ott, E., Antonsen, T.M., Long time evolution of phase oscillator systems. Chaos, 19(2), 2009, 023117, 10.1063/1.3136851.
243. [243] Martens, E.A., Barreto, E., Strogatz, S.H., Ott, E., So, P., Antonsen, T.M., Exact results for the Kuramoto model with a bimodal frequency distribution. Phys. Rev. E, 79(2), 2009, 026204, 10.1103/PhysRevE.79.026204.
244. [244] Pikovsky, A.S., Rosenblum, M.G., Dynamics of heterogeneous oscillator ensembles in terms of collective variables. Physica D 240:9–10 (2011), 872–881, 10.1016/j.physd.2011.01.002.
245. [245] Watts, D.J., Strogatz, S.H., Collective dynamics of ‘small-world’ networks. Nature 393 (1998), 440–442, 10.1038/30918.
246. [246] Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U., Complex networks: Structure and dynamics. Phys. Rep. 424:4–5 (2006), 175–308, 10.1016/j.physrep.2005.10.009.
247. [247] Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C., Synchronization in complex networks. Phys. Rep. 469:3 (2008), 93–153, 10.1016/j.physrep.2008.09.002.
248. [248] Barrat, A., Barthlemy, M., Vespignani, A., Dynamical Processes on Complex Networks. first ed., 2008, Cambridge University Press, New York, NY, USA.
249. [249] Boccaletti, S., Bianconi, G., Criado, R., del Genio, C., Gómez-Gardeñes, J., Romance, M., Sendiña-Nadal, I., Wang, Z., Zanin, M., The structure and dynamics of multilayer networks. Phys. Rep. 544:1 (2014), 1–122, 10.1016/j.physrep.2014.07.001.
250. [250] Jalan, S., Amritkar, R.E., Self-organized and driven phase synchronization in coupled maps. Phys. Rev. Lett., 90(1), 2003, 014101, 10.1103/PhysRevLett.90.014101.
251. [251] Huang, L., Chen, Q., Lai, Y.-c., Pecora, L.M., Generic behavior of master-stability functions in coupled nonlinear dynamical systems. Phys. Rev. E, 80(3), 2009, 036204, 10.1103/PhysRevE.80.036204.
252. [252] Barahona, M., Pecora, L.M., Synchronization in small-world systems. Phys. Rev. Lett., 89, 2002, 054101, 10.1103/PhysRevLett.89.054101.
253. [253] Belykh, V.N., Belykh, I.V., Hasler, M., Connection graph stability method for synchronized coupled chaotic systems. Physica D 195:1–2 (2004), 159–187, 10.1016/j.physd.2004.03.012.
254. [254] Donetti, L., Hurtado, P.I., Muñoz, M.A., Entangled networks, synchronization, and optimal network topology. Phys. Rev. Lett., 95(18), 2005, 188701, 10.1103/PhysRevLett.95.188701.
255. [255] Belykh, I., de Lange, E., Hasler, M., Synchronization of bursting neurons: What matters in the network topology. Phys. Rev. Lett., 94(18), 2005, 188101, 10.1103/PhysRevLett.94.188101.
256. [256] Toönjes, R., Masuda, N., Kori, H., Synchronization transition of identical phase oscillators in a directed small-world network. Chaos, 20(3), 2010, 033108, 10.1063/1.3476316.
257. [257] Nishikawa, T., Motter, A.E., Lai, Y.-C., Hoppensteadt, F.C., Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?. Phys. Rev. Lett., 91(1), 2003, 014101, 10.1103/PhysRevLett.91.014101.
258. [258] Goh, K.-I., Kahng, B., Kim, D., Spectra and eigenvectors of scale-free networks. Phys. Rev. E, 64(5), 2001, 051903, 10.1103/PhysRevE.64.051903.
259. [259] Motter, A.E., Zhou, C.S., Kurths, J., Enhancing complex-network synchronization. Europhys. Lett. 69:3 (2005), 334–340, 10.1209/epl/i2004-10365-4.
260. [260] Motter, A.E., Zhou, C., Kurths, J., Network synchronization, diffusion, and the paradox of heterogeneity. Phys. Rev. E, 71(1), 2005, 016116, 10.1103/PhysRevE.71.016116.
261. [261] Chavez, M., Hwang, D.-U., Amann, A., Hentschel, H.G.E., Boccaletti, S., Synchronization is enhanced in weighted complex networks. Phys. Rev. Lett., 94(21), 2005, 218701, 10.1103/PhysRevLett.94.218701.
262. [262] Hwang, D.-U., Chavez, M., Amann, A., Boccaletti, S., Synchronization in complex networks with age ordering. Phys. Rev. Lett., 94(13), 2005, 138701, 10.1103/PhysRevLett.94.138701.
263. [263] Zhou, C., Motter, A.E., Kurths, J., Universality in the synchronization of weighted random networks. Phys. Rev. Lett., 96(3), 2006, 034101, 10.1103/PhysRevLett.96.034101.
264. [264] Chavez, M., Hwang, D.-U., Martinerie, J., Boccaletti, S., Degree mixing and the enhancement of synchronization in complex weighted networks. Phys. Rev. E, 74(6), 2006, 066107, 10.1103/PhysRevE.74.066107.
265. [265] Sorrentino, F., di Bernardo, M., Cuéllar, G.H., Boccaletti, S., Synchronization in weighted scale-free networks with degree2˘013degree correlation. Physica D 224:1–2 (2006), 123–129, 10.1016/j.physd.2006.09.030.
266. [266] Di Bernardo, M., Garofalo, F., Sorrentino, F., Effects of degree correlation on the synchronization of networks of oscillators. Int. J. Bifurcation Chaos 17:10 (2007), 3499–3506, 10.1142/S0218127407019263.
267. [267] Sorrentino, F., Pecora, L.M., Hagerstrom, A.M., Murphy, T.E., Roy, R., Complete characterization of the stability of cluster synchronization in complex dynamical networks. Sci. Adv., 2(4), 2016, e1501737, 10.1126/sciadv.1501737.
268. [268] Lodato, I., Boccaletti, S., Latora, V., Synchronization properties of network motifs. Europhys. Lett., 78(2), 2007, 28001, 10.1209/0295-5075/78/28001.
269. [269] Do, A.-L., Boccaletti, S., Gross, T., Graphical notation reveals topological stability criteria for collective dynamics in complex networks. Phys. Rev. Lett., 108, 2012, 194102, 10.1103/PhysRevLett.108.194102.
270. [270] Gross, T., Blasius, B., Adaptive coevolutionary networks: a review. J. R. Soc. Interface 5:20 (2008), 259–271, 10.1098/rsif.2007.1229.
271. [271] Sorrentino, F., Ott, E., Adaptive synchronization of dynamics on evolving complex networks. Phys. Rev. Lett., 100(11), 2008, 114101, 10.1103/PhysRevLett.100.114101.
272. [272] Yuan, W.-J., Zhou, J.-F., Li, Q., Chen, D.-B., Wang, Z., Spontaneous scale-free structure in adaptive networks with synchronously dynamical linking. Phys. Rev. E, 88(2), 2013, 022818, 10.1103/PhysRevE.88.022818.
273. [273] Almendral, J.A., Sendiña-Nadal, I., Yu, D., Leyva, I., Boccaletti, S., Regulating synchronous states of complex networks by pinning interaction with an external node. Phys. Rev. E, 80(6), 2009, 066111, 10.1103/PhysRevE.80.066111.
274. [274] Sorrentino, F., di Bernardo, M., Garofalo, F., Chen, G., Controllability of complex networks via pinning. Phys. Rev. E, 75(4), 2007, 046103, 10.1103/PhysRevE.75.046103.
275. [275] Josić, K., Török, A., Network architecture and spatio-temporally symmetric dynamics. Physica D 224:1–2 (2006), 52–68, 10.1016/j.physd.2006.09.024.
276. [276] Belykh, V.N., Osipov, G.V., Petrov, V.S., Suykens, J.A.K., Vandewalle, J., Cluster synchronization in oscillatory networks. Chaos, 18(3), 2008, 037106, 10.1063/1.2956986.
277. [277] Belykh, I., Hasler, M., Mesoscale and clusters of synchrony in networks of bursting neurons. Chaos, 21(1), 2011, 016106, 10.1063/1.3563581.
278. [278] Poel, W., Zakharova, A., Schöll, E., Partial synchronization and partial amplitude death in mesoscale network motifs. Phys. Rev. E, 91(2), 2015, 022915, 10.1103/PhysRevE.91.022915.
279. [279] Pecora, L.M., Sorrentino, F., Hagerstrom, A.M., Murphy, T.E., Roy, R., Cluster synchronization and isolated desynchronization in complex networks with symmetries. Nature Commun., 5, 2014, 4079, 10.1038/ncomms5079.
280. [280] Fu, C., Zhang, H., Zhan, M., Wang, X., Synchronous patterns in complex systems. Phys. Rev. E, 85(6), 2012, 066208, 10.1103/PhysRevE.85.066208.
281. [281] Lin, W., Fan, H., Wang, Y., Ying, H., Wang, X., Controlling synchronous patterns in complex networks. Phys. Rev. E, 93(4), 2016, 042209, 10.1103/PhysRevE.93.042209.
282. [282] Nicosia, V., Valencia, M., Chavez, M., Díaz-Guilera, A., Latora, V., Remote synchronization reveals network symmetries and functional modules. Phys. Rev. Lett., 110(17), 2013, 174102, 10.1103/PhysRevLett.110.174102.
283. [283] Fortunato, S., Community detection in graphs. Phys. Rep. 486:3–5 (2010), 75–174, 10.1016/j.physrep.2009.11.002.
284. [284] Park, K., Lai, Y.-C., Gupte, S., Kim, J.-W., Synchronization in complex networks with a modular structure. Chaos, 16(1), 2006, 015105, 10.1063/1.2154881.
285. [285] Zhao, M., Zhou, C., Lü, J., Lai, C.H., Competition between intra-community and inter-community synchronization and relevance in brain cortical networks. Phys. Rev. E, 84(1), 2011, 016109, 10.1103/PhysRevE.84.016109.
286. [286] Aguirre, J., Sevilla-Escoboza, R., Gutiérrez, R., Papo, D., Buldú, J.M., Synchronization of interconnected networks: The role of connector nodes. Phys. Rev. Lett., 112(24), 2014, 248701, 10.1103/PhysRevLett.112.248701.
287. [287] Buscarino, A., Frasca, M., Gambuzza, L.V., Hövel, P., Chimera states in time-varying complex networks. Phys. Rev. E, 91(2), 2015, 022817, 10.1103/PhysRevE.91.022817.
288. [288] Zhu, Y., Zheng, Z., Yang, J., Chimera states on complex networks. Phys. Rev. E, 89(2), 2014, 022914, 10.1103/PhysRevE.89.022914.
289. [289] Niebur, E., Schuster, H.G., Kammen, D.M., Koch, C., Oscillator-phase coupling for different two-dimensional network connectivities. Phys. Rev. A 44:10 (1991), 6895–6904, 10.1103/PhysRevA.44.6895.
290. [290] Gómez-Gardeñes, J., Moreno, Y., Arenas, A., Synchronizability determined by coupling strengths and topology on complex networks. Phys. Rev. E, 75, 2007, 066106, 10.1103/PhysRevE.75.066106.
291. [291] Ichinomiya, T., Frequency synchronization in a random oscillator network. Phys. Rev. E, 70, 2004, 026116, 10.1103/PhysRevE.70.026116.
292. [292] Restrepo, J.G., Ott, E., Hunt, B.R., Onset of synchronization in large networks of coupled oscillators. Phys. Rev. E, 71(3), 2005, 036151, 10.1103/PhysRevE.71.036151.
293. [293] Sonnenschein, B., Schimansky-Geier, L., Onset of synchronization in complex networks of noisy oscillators. Phys. Rev. E, 85(5), 2012, 051116, 10.1103/PhysRevE.85.051116.
294. [294] Hong, H., Choi, M.Y., Kim, B.J., Synchronization on small-world networks. Phys. Rev. E, 65(2), 2002, 026139, 10.1103/PhysRevE.65.026139.
295. [295] Moreno, Y., Pacheco, A.F., Synchronization of Kuramoto oscillators in scale-free networks. Europhys. Lett. 68:4 (2004), 603–609, 10.1209/epl/i2004-10238-x.
296. [296] Lee, D.-S., Synchronization transition in scale-free networks: Clusters of synchrony. Phys. Rev. E, 72(2), 2005, 026208, 10.1103/PhysRevE.72.026208.
297. [297] Oh, E., Rho, K., Hong, H., Kahng, B., Modular synchronization in complex networks. Phys. Rev. E, 72(4), 2005, 047101, 10.1103/PhysRevE.72.047101.
298. [298] McGraw, P.N., Menzinger, M., Clustering and the synchronization of oscillator networks. Phys. Rev. E, 72(1), 2005, 015101, 10.1103/PhysRevE.72.015101.
299. [299] Sorrentino, F., Ott, E., Network synchronization of groups. Phys. Rev. E, 76(5), 2007, 056114, 10.1103/PhysRevE.76.056114.
300. [300] Li, D., Leyva, I., Almendral, J.A., Sendiña-Nadal, I., Buldú, J.M., Havlin, S., Boccaletti, S., Synchronization interfaces and overlapping communities in complex networks. Phys. Rev. Lett., 101(16), 2008, 168701, 10.1103/PhysRevLett.101.168701.
301. [301] Rad, A.A., Sendiña-Nadal, I., Papo, D., Zanin, M., Buldú, J.M., del Pozo, F., Boccaletti, S., Topological measure locating the effective crossover between segregation and integration in a modular network. Phys. Rev. Lett., 108(22), 2012, 228701, 10.1103/PhysRevLett.108.228701.
302. [302] Gómez-Gardeñes, J., Moreno, Y., Arenas, A., Paths to synchronization on complex networks. Phys. Rev. Lett., 98, 2007, 034101, 10.1103/PhysRevLett.98.034101.
303. [303] Sendiña-Nadal, I., Ofran, Y., Almendral, J.A., Buldú, J.M., Leyva, I., Li, D., Havlin, S., Boccaletti, S., Unveiling protein functions through the dynamics of the interaction network. PLoS One, 6(3), 2011, e17679, 10.1371/journal.pone.0017679.
304. [304] Bergner, A., Frasca, M., Sciuto, G., Buscarino, A., Ngamga, E.J., Fortuna, L., Kurths, J., Remote synchronization in star networks. Phys. Rev. E, 85(2), 2012, 026208, 10.1103/PhysRevE.85.026208.
305. [305] Gambuzza, L.V., Cardillo, A., Fiasconaro, A., Fortuna, L., Gómez-Gardeñes, J., Frasca, M., Analysis of remote synchronization in complex networks. Chaos, 23(4), 2013, 043103, 10.1063/1.4824312.
306. [306] Gambuzza, L.V., Frasca, M., Fortuna, L., Boccaletti, S., Inhomogeneity induces relay synchronization in complex networks. Phys. Rev. E, 93(4), 2016, 042203, 10.1103/PhysRevE.93.042203.
307. [307] Gambuzza, L.V., Gómez-Gardeñes, J., Frasca, M., Amplitude dynamics favors synchronization in complex networks. Sci. Rep., 6, 2016, 24915, 10.1038/srep24915.
308. [308] De Domenico, M., Solé-Ribalta, A., Cozzo, E., Kivelä, M., Moreno, Y., Porter, M.A., Gómez, S., Arenas, A., Mathematical formulation of multilayer networks. Phys. Rev. X, 3, 2013, 041022, 10.1103/PhysRevX.3.041022.
309. [309] Gambuzza, L.V., Frasca, M., Gómez-Gardeñes, J., Intra-layer synchronization in multiplex networks. Europhys. Lett., 110(2), 2015, 20010, 10.1209/0295-5075/110/20010.
310. [310] Gutiérrez, R., Sendiña Nadal, I., Zanin, M., Papo, D., Boccaletti, S., Targeting the dynamics of complex networks. Sci. Rep., 2, 2012, 396, 10.1038/srep00396.
311. [311] Sevilla-Escoboza, R., Sendiña-Nadal, I., Leyva, I., Gutiérrez, R., Buldú, J.M., Boccaletti, S., Inter-layer synchronization in multiplex networks of identical layers. Chaos, 26(6), 2016, 065304, 10.1063/1.4952967.
312. [312] Louzada, V.H.P., Araújo, N.a.M., Andrade, J.S., Herrmann, H.J., Breathing synchronization in interconnected networks. Sci. Rep., 3, 2013, 3289, 10.1038/srep03289.
313. [313] Lago-Fernández, L.F., Huerta, R., Corbacho, F., Sigüenza, J.A., Fast response and temporal coherent oscillations in small-world networks. Phys. Rev. Lett. 84 (2000), 2758–2761, 10.1103/PhysRevLett.84.2758.
314. [314] Lago-Fernández, L.F., Corbacho, F.J., Huerta, R., Connection topology dependence of synchronization of neural assemblies on class 1 and 2 excitability. Neural Netw. 14:6–7 (2001), 687–696, 10.1016/S0893-6080(01)00032-6.
315. [315] Arenas, A., Díaz-Guilera, A., Pérez-Vicente, C.J., Synchronization reveals topological scales in complex networks. Phys. Rev. Lett., 96(11), 2006, 114102, 10.1103/PhysRevLett.96.114102.
316. [316] Boccaletti, S., Ivanchenko, M., Latora, V., Pluchino, A., Rapisarda, A., Detecting complex network modularity by dynamical clustering. Phys. Rev. E, 75(4), 2007, 045102, 10.1103/PhysRevE.75.045102.
317. [317] Girón, A., Saiz, H., Bacelar, F.S., Andrade, R.F.S., Gómez-Gardeñes, J., Synchronization unveils the organization of ecological networks with positive and negative interactions. Chaos, 26(6), 2016, 065302, 10.1063/1.4952960.
318. [318] Leyva, I., Sendiña-Nadal, I., Almendral, J., Sanjuan, M., Sparse repulsive coupling enhances synchronization in complex networks. Phys. Rev. E, 74, 2006, 056112(7), 10.1103/PhysRevE.74.056112.
319. [319] Sendiña-Nadal, I., Buldú, J.M., Leyva, I., Boccaletti, S., Phase locking induces scale-free topologies in networks of coupled oscillators. PLoS One, 3(7), 2008, e2644, 10.1371/journal.pone.0002644.
320. [320] Aoki, T., Aoyagi, T., Co-evolution of phases and connection strengths in a network of phase oscillators. Phys. Rev. Lett., 102(3), 2009, 034101, 10.1103/PhysRevLett.102.034101.
321. [321] Aoki, T., Aoyagi, T., Self-organized network of phase oscillators coupled by activity-dependent interactions. Phys. Rev. E, 84(6), 2011, 066109, 10.1103/PhysRevE.84.066109.
322. [322] Gutiérrez, R., Amann, A., Assenza, S., Gómez-Gardeñes, J., Latora, V., Boccaletti, S., Emerging meso- and macroscales from synchronization of adaptive networks. Phys. Rev. Lett., 107(23), 2011, 234103, 10.1103/PhysRevLett.107.234103.
323. [323] Assenza, S., Gutiérrez, R., Gómez-Gardeñes, J., Latora, V., Boccaletti, S., Emergence of structural patterns out of synchronization in networks with competitive interactions. Sci. Rep., 1, 2011, 99, 10.1038/srep00099.
324. [324] Avalos-Gaytán, V., Almendral, J.A., Papo, D., Schaeffer, S.E., Boccaletti, S., Assortative and modular networks are shaped by adaptive synchronization processes. Phys. Rev. E, 86(1), 2012, 015101, 10.1103/PhysRevE.86.015101.
325. [325] Makarov, V., Koronovskii, A., Maksimenko, V., Hramov, A., Moskalenko, O., Buldú, J., Boccaletti, S., Emergence of a multilayer structure in adaptive networks of phase oscillators. Chaos Solitons Fractal 84 (2016), 23–30, 10.1016/j.chaos.2015.12.022.
326. [326] Maistrenko, Y., Popovych, O., Burylko, O., Tass, P.A., Mechanism of desynchronization in the finite-dimensional Kuramoto model. Phys. Rev. Lett., 93, 2004, 084102, 10.1103/PhysRevLett.93.084102.
327. [327] van Hemmen, J.L., Wreszinski, W.F., Lyapunov function for the Kuramoto model of nonlinearly coupled oscillators. J. Stat. Phys. 72:1 (1993), 145–166, 10.1007/BF01048044.
328. [328] Daido, H., Onset of cooperative entrainment in limit-cycle oscillators with uniform all-to-all interactions: bifurcation of the order function. Physica D 91:1 (1996), 24–66, 10.1016/0167-2789(95)00260-X.
329. [329] Pluchino, A., Rapisarda, A., Metastability in the Hamiltonian mean field model and Kuramoto model. Physica A 365:1 (2006), 184–189, 10.1016/j.physa.2006.01.039.
330. [330] Basnarkov, L., Urumov, V., Phase transitions in the Kuramoto model. Phys. Rev. E, 76, 2007, 057201, 10.1103/PhysRevE.76.057201.
331. [331] Basnarkov, L., Urumov, V., Kuramoto model with asymmetric distribution of natural frequencies. Phys. Rev. E, 78, 2008, 011113, 10.1103/PhysRevE.78.011113.
332. [332] Ermentrout, G.B., Synchronization in a pool of mutually coupled oscillators with random frequencies. J. Math. Biol. 22:1 (1985), 1–9, 10.1007/BF00276542.
333. [333] Sakaguchi, H., Kuramoto, Y., A soluble active rotater model showing phase transitions via mutual entertainment. Progr. Theoret. Phys. 76:3 (1986), 576–581, 10.1143/PTP.76.576.
334. [334] Crawford, J.D., Amplitude expansions for instabilities in populations of globally-coupled oscillators. J. Stat. Phys. 74:5 (1994), 1047–1084, 10.1007/BF02188217.
335. [335] Pazó, D., Montbrió, E., Existence of hysteresis in the Kuramoto model with bimodal frequency distributions. Phys. Rev. E, 80(4), 2009, 046215, 10.1103/PhysRevE.80.046215.
336. [336] Sakaguchi, H., Cooperative phenomena in coupled oscillator systems under external fields. Progr. Theoret. Phys. 79:1 (1988), 39–46, 10.1143/PTP.79.39.
337. [337] Strogatz, S.H., Mirollo, R.E., Stability of incoherence in a population of coupled oscillators. J. Stat. Phys. 63:3 (1991), 613–635, 10.1007/BF01029202.
338. [338] Strogatz, S.H., Mirollo, R.E., Matthews, P.C., Coupled nonlinear oscillators below the synchronization threshold: Relaxation by generalized Landau damping. Phys. Rev. Lett. 68 (1992), 2730–2733, 10.1103/PhysRevLett.68.2730.
339. [339] Okuda, K., Kuramoto, Y., Mutual entrainment between populations of coupled oscillators. Progr. Theoret. Phys. 86:6 (1991), 1159–1176, 10.1143/ptp/86.6.1159.
340. [340] Bonilla, L.L., Neu, J.C., Spigler, R., Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators. J. Stat. Phys. 67:1 (1992), 313–330, 10.1007/BF01049037.
341. [341] Acebrón, J.A., Bonilla, L.L., De Leo, S., Spigler, R., Breaking the symmetry in bimodal frequency distributions of globally coupled oscillators. Phys. Rev. E 57 (1998), 5287–5290, 10.1103/PhysRevE.57.5287.
342. [342] Balmforth, N.J., Sassi, R., A shocking display of synchrony. Physica D 143:1–4 (2000), 21–55, 10.1016/S0167-2789(00)00095-6.
343. [343] Cohen, A.H., Holmes, P.J., Rand, R.H., The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: A mathematical model. J. Math. Biol. 13:3 (1982), 345–369, 10.1007/BF00276069.
344. [344] Sakaguchi, H., Shinomoto, S., Kuramoto, Y., Local and grobal self-entrainments in oscillator lattices. Progr. Theoret. Phys. 77:5 (1987), 1005–1010, 10.1143/PTP.77.1005.
345. [345] Daido, H., Lower critical dimension for populations of oscillators with randomly distributed frequencies: A renormalization-group analysis. Phys. Rev. Lett. 61 (1988), 231–234, 10.1103/PhysRevLett.61.231.
346. [346] Strogatz, S.H., Mirollo, R.E., Phase-locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies. Physica D 31:2 (1988), 143–168, 10.1016/0167-2789(88)90074-7.
347. [347] Daido, H., Population dynamics of randomly interacting self-oscillators. I: Tractable models without frustration. Progress of Theoretical Physics 77:3 (1987), 622–634, 10.1143/PTP.77.622 arXiv:http://ptp.oxfordjournals.org/content/77/3/622.full.pdf+html.
348. [348] Daido, H., Quasientrainment and slow relaxation in a population of oscillators with random and frustrated interactions. Phys. Rev. Lett., 68(7), 1992, 1073, 10.1103/PhysRevLett.68.1073.
349. [349] Lumer, E.D., Huberman, B.A., Hierarchical dynamics in large assemblies of interacting oscillators. Phys. Lett. A 160:3 (1991), 227–232, 10.1016/0375-9601(91)90767-3.
350. [350] A. Jadbabaie, N. Motee, M. Barahona, On the stability of the Kuramoto model of coupled nonlinear oscillators, in: American Control Conference, 2004. Proceedings of the 2004, vol. 5, 2004, pp. 4296–4301.
351. [351] Wiesenfeld, K., Colet, P., Strogatz, S.H., Synchronization transitions in a disordered josephson series array. Phys. Rev. Lett. 76:3 (1996), 404–407, 10.1103/PhysRevLett.76.404.
352. [352] Wiesenfeld, K., Colet, P., Strogatz, S.H., Frequency locking in Josephson arrays: Connection with the Kuramoto model. Phys. Rev. E 57 (1998), 1563–1569, 10.1103/PhysRevE.57.1563.
353. [353] Gómez-Gardeñes, J., Moreno, Y., From scale-free to Erdos-Rényi networks. Phys. Rev. E, 73, 2006, 056124, 10.1103/PhysRevE.73.056124.
354. [354] Pereira, T., Eroglu, D., Bagci, G.B., Tirnakli, U., Jensen, H.J., Connectivity-driven coherence in complex networks. Phys. Rev. Lett., 110, 2013, 234103, 10.1103/PhysRevLett.110.234103.
355. [355] Watanabe, S., Strogatz, S.H., Integrability of a globally coupled oscillator array. Phys. Rev. Lett. 70 (1993), 2391–2394, 10.1103/PhysRevLett.70.2391.
356. [356] Vlasov, V., Zou, Y., Pereira, T., Explosive synchronization is discontinuous. Phys. Rev. E, 92(1), 2015, 012904, 10.1103/PhysRevE.92.012904.
357. [357] Xu, C., Gao, J., Sun, Y., Huang, X., Zheng, Z., Explosive or continuous: Incoherent state determines the route to synchronization. Sci. Rep., 5, 2015, 12039, 10.1038/srep12039.
358. [358] Jiang, S., Tang, S., Pei, S., Fang, W., Zheng, Z., Low dimensional behavior of explosive synchronization on star graphs. J. Stat. Mech., 2015(10), 2015, P10007, 10.1088/1742-5468/2015/10/P10007.
359. [359] Coutinho, B.C., Goltsev, A.V., Dorogovtsev, S.N., Mendes, J.F.F., Kuramoto model with frequency-degree correlations on complex networks. Phys. Rev. E, 87(3), 2013, 032106, 10.1103/PhysRevE.87.032106.
360. [360] Peron, T.K.D., Rodrigues, F.A., Determination of the critical coupling of explosive synchronization transitions in scale-free networks by mean-field approximations. Phys. Rev. E, 86(5), 2012, 056108, 10.1103/PhysRevE.86.056108.
361. [361] Skardal, P.S., Sun, J., Taylor, D., Restrepo, J.G., Effects of degree-frequency correlations on network synchronization: Universality and full phase-locking. Europhys. Lett., 101(2), 2013, 20001, 10.1209/0295-5075/101/20001.
362. [362] Pinto, R.S., Saa, A., Explosive synchronization with partial degree-frequency correlation. Phys. Rev. E, 91(2), 2015, 022818, 10.1103/PhysRevE.91.022818.
363. [363] Dan, Y., Jun-Zhong, Y., Effects of correlation between network structure and dynamics of oscillators on synchronization transition in a Kuramoto model on scale-free networks. Commun. Theor. Phys. 61:2 (2014), 197–202, 10.1088/0253-6102/61/2/09.
364. [364] Peron, T.K.D., Rodrigues, F.A., Explosive synchronization enhanced by time-delayed coupling. Phys. Rev. E, 86(1), 2012, 016102, 10.1103/PhysRevE.86.016102.
365. [365] Liu, W., Wu, Y., Xiao, J., Zhan, M., Effects of frequency-degree correlation on synchronization transition in scale-free networks. Europhys. Lett., 101(3), 2013, 38002, 10.1209/0295-5075/101/38002.
366. [366] Li, P., Zhang, K., Xu, X., Zhang, J., Small, M., Reexamination of explosive synchronization in scale-free networks: The effect of disassortativity. Phys. Rev. E, 87(4), 2013, 042803, 10.1103/PhysRevE.87.042803.
367. [367] Bender, E.A., Canfield, E., The asymptotic number of labeled graphs with given degree sequences. J. Combin. Theor. Ser. A 24:3 (1978), 296–307, 10.1016/0097-3165(78)90059-6.
368. [368] Newman, M.E.J., Mixing patterns in networks. Phys. Rev. E, 67, 2003, 026126, 10.1103/PhysRevE.67.026126.
369. [369] Xulvi-Brunet, R., Sokolov, I., Reshuffling scale-free networks: From random to assortative. Phys. Rev. E, 70(6), 2004, 066102, 10.1103/PhysRevE.70.066102.
370. [370] Zhu, L., Tian, L., Shi, D., Criterion for the emergence of explosive synchronization transitions in networks of phase oscillators. Phys. Rev. E, 88(4), 2013, 042921, 10.1103/PhysRevE.88.042921.
371. [371] Zhang, Y., Wan, W.-H., States and transitions in mixed networks. Front. Phys. 9:4 (2014), 523–528, 10.1007/s11467-014-0426-0.
372. [372] Zhu, L., Tian, L., Shi, D., Explosive transitions to synchronization in weighted static scale-free networks. Eur. Phys. J. B, 86(11), 2013, 451, 10.1140/epjb/e2013-40807-6.
373. [373] Hu, X., Boccaletti, S., Huang, W., Zhang, X., Liu, Z., Guan, S., Lai, C.-H., Exact solution for first-order synchronization transition in a generalized Kuramoto model. Sci. Rep., 4(4), 2014, 7262, 10.1038/srep07262.
374. [374] Xu, C., Sun, Y., Gao, J., Qiu, T., Zheng, Z., Guan, S., Synchronization of phase oscillators with frequency-weighted coupling. Sci. Rep., 6, 2016, 21926, 10.1038/srep21926.
375. [375] Zhou, W., Chen, L., Bi, H., Hu, X., Liu, Z., Guan, S., Explosive synchronization with asymmetric frequency distribution. Phys. Rev. E, 92(1), 2015, 012812, 10.1103/PhysRevE.92.012812.
376. [376] Navas, A., Villacorta-Atienza, J.A., Leyva, I., Almendral, J.A., Sendiña Nadal, I., Boccaletti, S., Effective centrality and explosive synchronization in complex networks. Phys. Rev. E, 92, 2015, 062820, 10.1103/PhysRevE.92.062820.
377. [377] Skardal, P.S., Arenas, A., Disorder induces explosive synchronization. Phys. Rev. E, 89(6), 2014, 062811, 10.1103/PhysRevE.89.062811.
378. [378] Gupta, S., Campa, A., Ruffo, S., Nonequilibrium first-order phase transition in coupled oscillator systems with inertia and noise. Phys. Rev. E, 89(2), 2014, 022123, 10.1103/PhysRevE.89.022123.
379. [379] Chavanis, P.-H., The Brownian mean field model. Eur. Phys. J. B 87:5 (2014), 1–33, 10.1140/epjb/e2014-40586-6.
380. [380] Sonnenschein, B., Sagués, F., Schimansky-Geier, L., Networks of noisy oscillators with correlated degree and frequency dispersion. Eur. Phys. J. B, 86(1), 2013, 12, 10.1140/epjb/e2012-31026-x.
381. [381] He, D., Shi, P., Stone, L., Noise-induced synchronization in realistic models. Phys. Rev. E, 67(2), 2003, 027201, 10.1103/PhysRevE.67.027201.
382. [382] Zhou, C., Kurths, J., Noise-induced phase synchronization and synchronization transitions in chaotic oscillators. Phys. Rev. Lett., 88(23), 2002, 230602, 10.1103/PhysRevLett.88.230602.
383. [383] Toral, R., Mirasso, C.R., Hernández-Garcıa, E., Piro, O., Analytical and numerical studies of noise-induced synchronization of chaotic systems. Chaos 11:3 (2001), 665–673, 10.1063/1.1386397.
384. [384] Neiman, A.B., Russell, D.F., Synchronization of noise-induced bursts in noncoupled sensory neurons. Phys. Rev. Lett., 88(13), 2002, 138103, 10.1103/PhysRevLett.88.138103.
385. [385] Sanchez, E., Matias, M., Perez-Muñuzuri, V., Analysis of synchronization of chaotic systems by noise: an experimental study. Phys. Rev. E, 56(4), 1997, 4068, 10.1103/PhysRevE.56.4068.
386. [386] Baier, G., Santos, G.J.E., Perales, H., Rivera, M., Müller, M., Leder, R., Parmananda, P., Self-exciting chaos as a dynamic model for irregular neural spiking. Phys. Rev. E, 62(6), 2000, R7579, 10.1103/PhysRevE.62.R7579.
387. [387] Börgers, C., Kopell, N., Synchronization in networks of excitatory and inhibitory neurons with sparse, random connectivity. Neural Comput. 15:3 (2003), 509–538, 10.1162/089976603321192059.
388. [388] Qu, Z., Shiferaw, Y., Weiss, J.N., Nonlinear dynamics of cardiac excitation-contraction coupling: an iterated map study. Phys. Rev. E, 75(1), 2007, 011927, 10.1103/PhysRevE.75.011927.
389. [389] Galam, S., Contrarian deterministic effects on opinion dynamics: “the hung elections scenario”. Physica A 333 (2004), 453–460, 10.1016/j.physa.2003.10.041.
390. [390] de la Lama, M.S., López, J.M., Wio, H.S., Spontaneous emergence of contrarian-like behaviour in an opinion spreading model. Europhys. Lett., 72(5), 2005, 851, 10.1209/epl/i2005-10299-3.
391. [391] Hong, H., Strogatz, S.H., Kuramoto model of coupled oscillators with positive and negative coupling parameters: An example of conformist and contrarian oscillators. Phys. Rev. Lett., 106, 2011, 054102, 10.1103/PhysRevLett.106.054102.
392. [392] Yuan, D., Zhang, M., Yang, J., Dynamics of the Kuramoto model in the presence of correlation between distributions of frequencies and coupling strengths. Phys. Rev. E, 89(1), 2014, 012910, 10.1103/PhysRevE.89.012910.
393. [393] Qiu, T., Boccaletti, S., Bonamassa, I., Zou, Y., Zhou, J., Liu, Z., Guan, S., Synchronization and Bellerophon state in conformists and contrarians oscillators. Sci. Rep., 6, 2016, 36713.
394. [394] Iatsenko, D., Petkoski, S., McClintock, P., Stefanovska, A., Stationary and traveling wave states of the Kuramoto model with an arbitrary distribution of frequencies and coupling strengths. Phys. Rev. Lett., 110(6), 2013, 064101, 10.1103/PhysRevLett.110.064101.
395. [395] Kuramoto, Y., Battogtokh, D., Coexistence of coherence and incoherence in nonlocally coupled phase oscillators. Nonlinear Phenom. Complex Syst. 5 (2002), 380–385.
396. [396] Shima, S.-i., Kuramoto, Y., Rotating spiral waves with phase-randomized core in nonlocally coupled oscillators. Phys. Rev. E, 69(3), 2004, 036213, 10.1103/PhysRevE.69.036213.
397. [397] Bi, H., Hu, X., Boccaletti, S., Wang, X., Zou, Y., Liu, Z., Guan, S., Coexistence of quantized, time dependent, clusters in globally coupled oscillators. Phys. Rev. Lett., 2016 in press.
398. [398] W. Zhou, Y. Zou, J. Zhou, S. Guan, Intermittent nonstationary clustering state in frequency-weighted Kuramoto model, submitted for publication.
399. [399] H. Bi, Y. Li, Y. Zou, J. Zhou, S. Guan, A nontrivial standing wave state in frequency-weighted Kuramoto model, submitted for publication.
400. [400] Jiang, X., Li, M., Zheng, Z., Ma, Y., Ma, L., Effect of externality in multiplex networks on one-layer synchronization. J. Korean Phys. Soc. 66:11 (2015), 1777–1782, 10.3938/jkps.66.1777.
401. [401] Su, G., Ruan, Z., Guan, S., Liu, Z., Explosive synchronization on co-evolving networks. Europhys. Lett., 103(4), 2013, 48004, 10.1209/0295-5075/103/48004.
402. [402] Barabási, A.-L., Albert, R., Emergence of scaling in random networks. Science 286:5439 (1999), 509–512, 10.1126/science.286.5439.509.
403. [403] M.M. Danziger, O.I. Moskalenko, S.A. Kurkin, X. Zhang, S. Havlin, S. Boccaletti, Explosive synchronization coexists with classical synchronization in the Kuramoto model, Chaos 26 (6). http://dx.doi.org/10.1063/1.4953345.
404. [404] Radicchi, F., Percolation in real interdependent networks. Nat. Phys. 11 (2015), 597–602, 10.1038/nphys3374.
405. [405] M. Amin, P.F. Schewe, Preventing blackouts, Sci. Am. 296.
406. [406] Nardelli, P.H., Rubido, N., Wang, C., Baptista, M.S., Pomalaza-Raez, C., Cardieri, P., Latva-aho, M., Models for the modern power grid. Eur. Phys. J. Spec. Top. 223 (2014), 2423–2437, 10.1140/epjst/e2014-02219-6.
407. [407] Chiang, H.-D., Chu, C.-C., Cauley, G., Direct stability analysis of electric power systems using energy functions: theory, applications, and perspective. Proc. IEEE 83:11 (1995), 1497–1529, 10.1109/5.481632.
408. [408] Filatrella, G., Nielsen, A.H., Pedersen, N.F., Analysis of a power grid using a kuramoto-like model. Eur. Phys. J. B 61:4 (2008), 485–491, 10.1140/epjb/e2008-00098-8.
409. [409] Chiang, H.-D., Dobson, I., Robcrt, J., Thorp, J.S., Fekih-ahmed, L., On voltage collapse in electric power systems. IEEE Trans. Power Syst. 5:2 (1990), 601–611, 10.1109/59.54571.
410. [410] Menck, P.J., Heitzig, J., Kurths, J., Schellnhuber, H.J., Menck, P.J., How dead ends undermine power grid stability. Nature Commun., 5, 2014, 3969, 10.1038/ncomms4969.
411. [411] Rohden, M., Sorge, A., Timme, M., Witthaut, D., Self-Organized synchronization in decentralized power grids. Phys. Rev. Lett., 109(6), 2012, 064101, 10.1103/PhysRevLett.109.064101.
412. [412] Rohden, M., Sorge, A., Witthaut, D., Timme, M., Impact of network topology on synchrony of oscillatory power grids. Chaos, 24(1), 2014, 013123, 10.1063/1.4865895.
413. [413] Lozano, S., Buzna, L., Díaz-Guilera, A., Role of network topology in the synchronization of power systems. Eur. Phys. J. B 85:7 (2012), 1–8, 10.1140/epjb/e2012-30209-9.
414. [414] Motter, A.E., Myers, S.A., Anghel, M., Nishikawa, T., Spontaneous synchrony in power-grid networks. Nat. Phys. 9:3 (2013), 191–197, 10.1038/nphys2535.
415. [415] Peron, T.K.D., Ji, P., Rodrigues, F.A., Kurths, J., Effects of assortative mixing in the second-order kuramoto model. Phys. Rev. E, 91, 2015, 052805, 10.1103/PhysRevE.91.052805.
416. [416] Olmi, S., Navas, A., Boccaletti, S., Torcini, A., Hysteretic transitions in the Kuramoto model with inertia. Phys. Rev. E, 90(4), 2014, 042905, 10.1103/PhysRevE.90.042905.
417. [417] Ji, P., Peron, T.K.D., Menck, P.J., Rodrigues, F.a., Kurths, J., Cluster explosive synchronization in complex networks. Phys. Rev. Lett., 110(21), 2013, 218701, 10.1103/PhysRevLett.110.218701.
418. [418] Ji, P., Peron, T.K.D., Rodrigues, F.A., Kurths, J., Analysis of cluster explosive synchronization in complex networks. Phys. Rev. E, 90(6), 2014, 062810, 10.1103/PhysRevE.90.062810.
419. [419] Rohden, M., Sorge, A., Timme, M., Witthaut, D., Self-organized synchronization in decentralized power grids. Phys. Rev. Lett., 109(6), 2012, 064101, 10.1103/PhysRevLett.109.064101.
420. [420] Buzsaki, G., Rhythms of the Brain. 2006, Oxford University Press, Oxford.
421. [421] Fell, J., Axmacher, N., The role of phase synchronization in memory processes. Nat. Rev. Neurosci. 12:2 (2011), 105–118, 10.1038/nrn2979.
422. [422] Kramer, M.A., Cash, S.S., Epilepsy as a disorder of cortical network organization. Neuroscientist 18:4 (2012), 360–372, 10.1177/1073858411422754.
423. [423] Yaffe, R.B., Borger, P., Megevand, P., Groppe, D.M., Kramer, M.a., Chu, C.J., Santaniello, S., Meisel, C., Mehta, A.D., Sarma, S.V., Physiology of functional and effective networks in epilepsy. Clin. Neurophysiol. 126:2 (2015), 227–236, 10.1016/j.clinph.2014.09.009.
424. [424] Ben-Jacob, E., Boccaletti, S., Pomyalov, A., Procaccia, I., Towle, V.L., Detecting and localizing the foci in human epileptic seizures. Chaos, 17(4), 2007, 043113, 10.1063/1.2805658.
425. [425] Guye, M., Régis, J., Tamura, M., Wendling, F., Mc Gonigal, A., Chauvel, P., Bartolomei, F., The role of corticothalamic coupling in human temporal lobe epilepsy. Brain 129:7 (2006), 1917–1928, 10.1093/brain/awl151.
426. [426] Perucca, P., Dubeau, F., Gotman, J., Intracranial electroencephalographic seizure-onset patterns: effect of underlying pathology. Brain 137:1 (2014), 183–196, 10.1093/brain/awt299.
427. [427] Schindler, K., Leung, H., Elger, C.E., Lehnertz, K., Assessing seizure dynamics by analysing the correlation structure of multichannel intracranial eeg. Brain 130:1 (2007), 65–77, 10.1093/brain/awl304.
428. [428] Friedman, E.B., Sun, Y., Moore, J.T., Hung, H.-T., Meng, Q.C., Perera, P., Joiner, W.J., Thomas, S.A., Eckenhoff, R.G., Sehgal, A., Kelz, M.B., A conserved behavioral state barrier impedes transitions between anesthetic-induced unconsciousness and wakefulness: Evidence for neural inertia. PLoS One, 5(7), 2010, e11903, 10.1371/journal.pone.0011903.
429. [429] Joiner, W.J., Friedman, E.B., Hung, H.-T., Koh, K., Sowcik, M., Sehgal, A., Kelz, M.B., Genetic and anatomical basis of the barrier separating wakefulness and anesthetic-induced unresponsiveness. PLoS Genetics, 9(9), 2013, e1003605, 10.1371/journal.pgen.1003605.
430. [430] Kim, M., Mashour, G.A., Blain-Moraes, S., Vanini, G., Tarnal, V., Janke, E., Hudetz, A.G., Lee, U., Functional and topological conditions for explosive synchronization develop in human brain networks with the onset of anesthetic-induced unconsciousness. Front. Comput. Neurosci., 10, 2016, 1, 10.3389/fncom.2016.00001.
431. [431] Nakao, H., Mikhailov, A.S., Diffusion-induced instability and chaos in random oscillator networks. Phys. Rev. E, 79, 2009, 036214, 10.1103/PhysRevE.79.036214.
432. [432] Bi, H., Hu, X., Zhang, X., Zou, Y., Liu, Z., Guan, S., Explosive oscillation death in coupled Stuart-Landau oscillators. Europhys. Lett., 108(5), 2014, 50003, 10.1209/0295-5075/108/50003.
433. [433] Matthews, P.C., Mirollo, R.E., Strogatz, S.H., Dynamics of a large system of coupled nonlinear oscillators. Physica D 52:2 (1991), 293–331, 10.1016/0167-2789(91)90129-W.
434. [434] Atay, F.M., Distributed delays facilitate amplitude death of coupled oscillators. Phys. Rev. Lett., 91, 2003, 094101, 10.1103/PhysRevLett.91.094101.
435. [435] Pisarchik, A.N., Jaimes-Reátegui, R., Villalobos-Salazar, J.R., García-López, J.H., Boccaletti, S., Synchronization of chaotic systems with coexisting attractors. Phys. Rev. Lett., 96, 2006, 244102, 10.1103/PhysRevLett.96.244102.
436. [436] Pisarchik, A.N., Jaimes-Reátegui, R., Sevilla-Escoboza, R., Boccaletti, S., Experimental approach to the study of complex network synchronization using a single oscillator. Phys. Rev. E, 79, 2009, 055202(R), 10.1103/PhysRevE.79.055202.
437. [437] Kumar, P., Verma, D.K., Parmananda, P., Boccaletti, S., Experimental evidence of explosive synchronization in mercury beating-heart oscillators. Phys. Rev. E, 91(6), 2015, 062909, 10.1103/PhysRevE.91.062909.
438. [438] Zhang, X., Guan, S., Zou, Y., Chen, X., Liu, Z., Suppressing explosive synchronization by contrarians. Europhys. Lett., 113(2), 2016, 28005, 10.1209/0295-5075/113/28005.
439. [439] Louzada, V., Araújo, N., Andrade, J. Jr., Herrmann, H., How to suppress undesired synchronization. Sci. Rep., 2, 2012, 658, 10.1038/srep00658.
440. [440] Restrepo, J.G., Ott, E., Hunt, B.R., Synchronization in large directed networks of coupled phase oscillators. Chaos, 16(1), 2006, 015107, 10.1063/1.2148388.
441. [441] Zanette, D.H., Synchronization and frustration in oscillator networks with attractive and repulsive interactions. Europhys. Lett., 72(2), 2005, 190, 10.1209/epl/i2005-10238-4.
442. [442] Freund, T., Buzsáki, G., Interneurons of the hippocampus. Hippocampus 6:4 (1996), 347–470 http://dx.doi.org/10.1002/(SICI)1098-1063(1996)6:4<347::AID-HIPO1>3.0.CO;2-I.
443. [443] Klausberger, T., Somogyi, P., Neuronal diversity and temporal dynamics: the unity of hippocampal circuit operations. Science 321:5885 (2008), 53–57, 10.1126/science.1149381.
444. [444] Zhang, X., Bi, H., Guan, S., Liu, J., Liu, Z., Model bridging chimera state and explosive synchronization. Phys. Rev. E, 94, 2016, 012204, 10.1103/PhysRevE.94.012204.
445. [445] Chen, L., Ghanbarnejad, F., Cai, W., Grassberger, P., Outbreaks of coinfections: The critical role of cooperativity. Europhys. Lett., 104(5), 2013, 50001, 10.1209/0295-5075/104/50001.
446. [446] Hébert-Dufresne, L., Althouse, B.M., Complex dynamics of synergistic coinfections on realistically clustered networks. Proc. Natl. Acad. Sci. 112:33 (2015), 10551–10556.
447. [447] Gómez-Gardeñes, J., Lotero, L., Taraskin, S., Pérez-Reche, F., Explosive contagion in networks. Sci. Rep., 6, 2016, 19767, 10.1038/srep19767.
448. [448] Majdandzic, A., Podobnik, B., Buldyrev, S.V., Kenett, D.Y., Havlin, S., Stanley, H.E., Spontaneous recovery in dynamical networks. Nat. Phys. 10:1 (2014), 34–38.
449. [449] H. Chen, C. Shen, H. Zhang, G. Li, Z. Hou, J. Kurths, Explosive Phase Transition in a Majority-Vote Model with Inertia, ArXiv e-prints, arXiv:1609.00469.