Controlling synchronous patterns in complex networks

Physical Review E

Volumn 93, Issue 4, 2016, Pages

  Lin, Weijie ^a,b   Fan, Huawei ^b   Wang, Ying ^b   Ying, Heping ^a   Wang, Xingang ^b  

^a ZHEJIANG UNIVERSITY   (China)

^b SHAANXI NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CIRCUIT OSCILLATIONS; NETWORKS (CIRCUITS); NUMERICAL METHODS;

CHAOTIC CIRCUITS; COUPLED CHAOTIC OSCILLATORS; NETWORK SYMMETRIES; PERMUTATION SYMMETRY; PINNING STRENGTH; REAL-WORLD NETWORKS; SYNCHRONIZATION PATTERNS; WEIGHTED NETWORKS;

COMPLEX NETWORKS;

EID: 84964515487     PISSN: 24700045     EISSN: 24700053     Source Type: Journal    
DOI: 10.1103/PhysRevE.93.042209     Document Type: Article

References (55)

1. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984).
2. A. S. Pikovsky, M. G. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Science (Cambridge University Press, Cambridge, 2001).
3. S. Strogatz, Sync: The Emerging Science of Spontaneous Order (Hyperion, New York, 2003).
4. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, Complex networks: Structure and dynamics, Phys. Rep. 424, 175 (2006). PRPLCM 0370-1573 10.1016/j.physrep.2005.10.009
5. A. Arenas, A. Diaz-Guilera, J. Kurths, Y. Moreno, and C. S. Zhou, Synchronization in complex networks, Phys. Rep. 469, 93 (2008). PRPLCM 0370-1573 10.1016/j.physrep.2008.09.002
6. L. M. Pecora and T. L. Carroll, Synchronization in Chaotic Systems, Phys. Rev. Lett. 64, 821 (1990). PRLTAO 0031-9007 10.1103/PhysRevLett.64.821
7. X. G. Wang, L. Huang, S. G. Guan, Y.-C. Lai, and C.-H. Lai, Onset of synchronization in complex gradient networks, Chaos 18, 037117 (2008). CHAOEH 1054-1500 10.1063/1.2964202
8. A. E. Motter, S. A. Myers, M. Anghel, and T. Nishikawa, Spontaneous synchrony in power-grid networks, Nat. Phys. 9, 191 (2013). 1745-2473 10.1038/nphys2535
9. E. R. Kandel, J. H. Schwartz, and T. M. Jessell, Principles of Neural Science (McGraw-Hill, New York, 2000).
10. E. Basar, Brain Function and Oscillation (Springer, New York, 1998).
11. V. N. Belykh and E. Mosekilde, One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures, Phys. Rev. E 54, 3196 (1996). 1063-651X 10.1103/PhysRevE.54.3196
12. M. Hasler, Yu. Maistrenko, and O. Popovych, Simple example of partial synchronizaiton of chaotic systems, Phys. Rev. E 58, 6843 (1998). 1063-651X 10.1103/PhysRevE.58.6843
13. Y. Zhang, G. Hu, H. A. Cerdeira, S. Chen, T. Braun, and Y. Yao, Partial synchronization and spontaneous spatial ordering in coupled chaotic systems, Phys. Rev. E 63, 026211 (2001). 1063-651X 10.1103/PhysRevE.63.026211
14. A. Pikovsky, O. Popovych, and Yu. Maistrenko, Resolving Clusters in Chaotic Ensembles of Globally Coupled Identical Oscillators, Phys. Rev. Lett. 87, 044102 (2001). PRLTAO 0031-9007 10.1103/PhysRevLett.87.044102
15. B. Ao and Z. G. Zheng, Partial synchronization on complex networks, Europhys. Lett. 74, 229 (2006). EULEEJ 0295-5075 10.1209/epl/i2005-10533-0
16. C. S. Zhou and J. Kurths, Hierarchical synchronization in complex networks with heterogeneous degrees, Chaos 16, 015104 (2006). CHAOEH 1054-1500 10.1063/1.2150381
17. F. Sorrentino, and E. Ott, Network synchronization of groups, Phys. Rev. E 76, 056114 (2007). PLEEE8 1539-3755 10.1103/PhysRevE.76.056114
18. T. Dahms, J. Lehnert, and E. Schöll, Cluster and group synchronization in delay-coupled networks, Phys. Rev. E 86, 016202 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.86.016202
19. V. Nicosia, M. Valencia, M. Chavez, A. Diaz-Guilera, and V. Latora, Remote Synchronization Reveals Network Symmetries and Functional Modules, Phys. Rev. Lett. 110, 174102 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.174102
20. C. Fu, Z. Deng, L. Huang, and X. G. Wang, Topological control of synchronous patterns in systems of networked chaotic oscillators, Phys. Rev. E 87, 032909 (2013). PLEEE8 1539-3755 10.1103/PhysRevE.87.032909
21. C. Fu, W. Lin, L. Huang, and X. G. Wang, Synchronization transition in networked chaotic oscillators: The viewpoint from partial synchronization, Phys. Rev. E 89, 052908 (2014). PLEEE8 1539-3755 10.1103/PhysRevE.89.052908
22. L. M. Pecora, F. Sorrentino, A. M. Hagerstrom, T. E. Murphy, and R. Roy, Cluster synchronization and isolated desynchronization in complex networks with symmetries, Nat. Commun. 5, 4079 (2014). 2041-1723 10.1038/ncomms5079
23. F. Sorrentino, L. M. Pecora, A. M. Hagerstrom, T. E. Murphy, and R. Roy, Complete characterization of stability of cluster synchronization in complex dynamical networks, arXiv:1507.04381.
24. D. J. Watts and S. H. Strogatz, Collective dynamics of smallworldnetworks, Nature (London) 393, 440 (1998). NATUAS 0028-0836 10.1038/30918
25. A.-L. Barabási and R. Albert, Emergence of scaling in random networks, Science 286, 509 (1999). SCIEAS 0036-8075 10.1126/science.286.5439.509
26. P. M. Gade and C.-K. Hu, Synchronous chaos in coupled map lattices with small-world interactions, Phys. Rev. E 62, 6409 (2000). 1063-651X 10.1103/PhysRevE.62.6409
27. M. Barahona and L. M. Pecora, Synchronization in Small-World Systems, Phys. Rev. Lett. 89, 054101 (2002). PRLTAO 0031-9007 10.1103/PhysRevLett.89.054101
28. T. Nishikawa, A. E. Motter, Y.-C. Lai, and F. C. Hoppensteadt, Heterogeneity in Oscillator Networks: Are Smaller Worlds Easier to Synchronize? Phys. Rev. Lett. 91, 014101 (2003). PRLTAO 0031-9007 10.1103/PhysRevLett.91.014101
29. A. E. Motter, C. Zhou, and J. Kurths, Weighted networks are more synchronizable: How and why, AIP Conf. Proc. 776, 201 (2005). APCPCS 0094-243X 10.1063/1.1985389
30. K. Park, L. Huang, and Y.-C. Lai, Desynchronization waves in small-world networks, Phys. Rev. E 75, 026211 (2007). PLEEE8 1539-3755 10.1103/PhysRevE.75.026211
31. X. G. Wang, S. Guan, Y.-C. Lai, B. Li, and C. H. Lai, Desynchronization and on-off intermittency in complex networks, Europhys. Lett. 88, 28001 (2009). EULEEJ 0295-5075 10.1209/0295-5075/88/28001
32. C. Fu, H. Zhang, M. Zhan, and X. G. Wang, Synchronous patterns in complex systems, Phys. Rev. E 85, 066208 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.85.066208
33. O. D'Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, Synchronization properties of network motifs: Influence of coupling delay and symmetry, Chaos 18, 037116 (2008). CHAOEH 1054-1500 10.1063/1.2953582
34. G. Russo and J. J. E. Slotine, Symmetries, stability, and control in nonlinear systems and networks, Phys. Rev. E 84, 041929 (2011). PLEEE8 1539-3755 10.1103/PhysRevE.84.041929
35. M. Golubitsky and I. Stewart, Recent advances in symmetric and network dynamics, Chaos 25, 097612 (2015). CHAOEH 1054-1500 10.1063/1.4918595
36. W. Stein, SAGE: Software for Algebra an Geometry Experimentation (2013) http://www.sagemath.org/sage/.
37. B. D. MacArthur and R. J. Sanchez-Garcia, and J. W. Anderson, On automorphism groups of networks, Discrete Appl. Math. 156, 3525 (2008). DAMADU 0166-218X 10.1016/j.dam.2008.04.008
38. R. Andersson, A. Johnston, and A. Fisahn, Dopamine D4 receptor activation increases hippocampal gamma oscillations by enhancing synchronization of fast-spiking interneurons, PLoS ONE 7, e40906 (2012). 1932-6203 10.1371/journal.pone.0040906
39. L. Yetnikoff, H. N. Lavezzi, R. A. Reichard, and D. S. Zahm, An update on the connections of the ventral mesencephalic dopaminergic complex, Neuroscience 282, 23 (2014). NRSCDN 0306-4522 10.1016/j.neuroscience.2014.04.010
40. M. Z. Jacobson and M. A. Delucchi, Providing all global energy with wind, water, and solar power, Part I: Technologies, energy resources, quantities and areas of infrastructure, and materials, Energy Policy 39, 1154 (2011). 0301-4215 10.1016/j.enpol.2010.11.040
41. S. Chatzivasileiadis, D. Ernst, and G. Andersson, The global grid, Renewable Energy 57, 372 (2013). RNENE3 0960-1481 10.1016/j.renene.2013.01.032
42. L. M. Pecora and T. L. Carroll, Synchronization of chaotic systems, Chaos 25, 097611 (2015). CHAOEH 1054-1500 10.1063/1.4917383
43. L. M. Pecora and T. L. Carroll, Master Stability Functions for Synchronized Coupled Systems, Phys. Rev. Lett. 80, 2109 (1998). PRLTAO 0031-9007 10.1103/PhysRevLett.80.2109
44. G. Hu, J. Z. Yang, and W. Liu, Instability and controllability of linearly coupled oscillators: Eigenvalue analysis, Phys. Rev. E 58, 4440 (1998). 1063-651X 10.1103/PhysRevE.58.4440
45. L. Huang, Q. Chen, Y.-C. Lai, and L. M. Pecora, Generic behavior of master-stability functions in coupled nonlinear dynamical systems, Phys. Rev. E 80, 036204 (2009). PLEEE8 1539-3755 10.1103/PhysRevE.80.036204
46. E. N. Lorenz, Deterministic nonperiodic flow, J. Atmos. Sci. 20, 130 (1963). JAHSAK 0022-4928 10.1175/1520-0469(1963)020%3C0130:DNF%3E2.0.CO;2
47. Nepal electricity authority annual report 2011, www.nea.org.np (2011).
48. M. P. Bahrman and B. K. Johnson, The ABCs of HVDC transmission technologies, IEEE Power & Energy Magazine 5, 32 (2007). 1540-7977 10.1109/MPAE.2007.329194
49. J. L. Hindmarsh and R. M. Rose, A model of neuronal bursting using three coupled first order differential equations, Proc. R. Soc. London B 221, 87 (1984). PRLBA4 0962-8452 10.1098/rspb.1984.0024
50. G. Ren, J. Tang, J. Ma, and Y. Xu, Detection of noise effect on coupled neuronal circuits, Commun. Nonlinear Sci. Numer. Simulat. 29, 170 (2015). 1007-5704 10.1016/j.cnsns.2015.05.001
51. X. F. Wang and G. R. Chen, Pinning control of scale-free dynamical networks, Physica A 310, 521 (2002). PHYADX 0378-4371 10.1016/S0378-4371(02)00772-0
52. F. Sorrentino, M. di Bernardo, F. Garofalo, and G. R. Chen, Controllability of complex networks via pinning, Phys. Rev. E 75, 046103 (2007). PLEEE8 1539-3755 10.1103/PhysRevE.75.046103
53. L. Yang, X. G. Wang, Y. Li, and Z. M. Sheng, On the pinning strategy of complex networks, Europhys. Lett. 92, 48002 (2010). EULEEJ 0295-5075 10.1209/0295-5075/92/48002
54. Y. Kuramoto and D. Battogtokh, Coexistence of coherence and incoherence in nonlocally coupled phase oscillators, Nonlinear Phenom. Complex Syst. 5, 380 (2002).
55. D. M. Abrams and S. H. Strogatz, Chimera States for Coupled Oscillators, Phys. Rev. Lett. 93, 174102 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.93.174102