Extracting topological features from dynamical measures in networks of Kuramoto oscillators

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 85, Issue 3, 2012, Pages

  Prignano, Luce ^a   Díaz Guilera, Albert ^a  

^a UNIVERSITY OF BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ADJACENCY MATRICES; CONNECTIVITY PATTERN; COUPLED OSCILLATORS; CRITICAL POINTS; DYNAMICAL BEHAVIORS; FREQUENCY DISTRIBUTIONS; GLOBAL DYNAMICS; HIERARCHICAL STRUCTURES; INCOHERENT STATE; INTERACTION NETWORKS; KURAMOTO MODELS; LOCAL FEATURE; NONEQUILIBRIUM TRANSITION; QUANTITATIVE STUDY; TOPOLOGICAL FEATURES; TOPOLOGICAL INFORMATION; TRANSITION POINT;

HETEROGENEOUS NETWORKS; MATHEMATICAL MODELS; SYNCHRONIZATION;

TOPOLOGY;

EID: 84859394562     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.036112     Document Type: Article

References (39)

1. R. Albert and A.-L. Barabási, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.47 74, 47 (2002).
2. M. E. J. Newman, SIAM Rev. SIREAD 0036-1445 10.1137/S003614450342480 45, 167 (2003).
3. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, Phys. Rep. 0370-1573 10.1016/j.physrep.2005.10.009 424, 175 (2006). (Pubitemid 43135890)
4. A. Barrat, M. Barthelemy, and A. Vespignani, Dynamical Processes on Complex Networks (Cambridge University Press, Cambridge, 2008).
5. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization (Cambridge University Press, Cambridge, 2001).
6. G. V. Osipov, J. Kurths, and C. Zhou, Synchronization in Oscillatory Networks (Springer, Berlin, 2007).
7. A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2008.09.002 469, 93 (2008).
8. A. T. Winfree, The Geometry of Biological Time (Springer, Berlin, 1980).
9. Y. Kuramoto, in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics Vol. 39, edited by, H. Araki, (Springer, New York, 1975), pp. 420-422.
10. J. A. Acebrón, L. L. Bonilla, C. J. Pérez-Vicente, F. Ritort, and R. Spigler, Rev. Mod. Phys. 0034-6861 10.1103/RevModPhys.77.137 77, 137 (2005). (Pubitemid 41490657)
11. There are, however, some limitations to these results, for instance, when the units are placed in regular lattices, such as one-dimensional rings, where other attractors different from the synchronized (equal phases) state may arise.
12. L. Buzna, S. Lozano, and A. Díaz-Guilera, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.066120 80, 066120 (2009).
13. H. Kori and A. S. Mikhailov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.254101 93, 254101 (2004). (Pubitemid 40121226)
14. F. Radicchi and H. Meyer-Ortmanns, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.73.036218 73, 036218 (2006).
15. F. Mori, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.108701 104, 108701 (2010).
16. A. Arenas, A. Díaz-Guilera, and C. J. Pérez-Vicente, Phys. D 0167-2789 10.1016/j.physd.2006.09.029 224, 27 (2006). (Pubitemid 44751205)
17. E. Ravasz and A.-L. Barabási, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.67.026112 67, 026112 (2003).
18. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, New York, 1984).
19. I. Sendiña-Nadal, J. Buldu, I. Leyva, and S. Boccaletti, PLoS ONE 1932-6203 10.1371/journal.pone.0002644 3, e2644 (2008).
20. i N, whose smallest possible value is N, which is the largest possible value for the bound.
21. It is not necessary to take into account the groups that do not include the pacemaker since the bound we obtain for ω p c when summing up n + 1 equations including the pacemaker or the remaining N - n + 1 (not including the pacemaker) is the same.
22. M. Girvan and M. E. J. Newman, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.122653799 99, 7821 (2002). (Pubitemid 34650963)
23. P. M. Gleiser and D. H. Zanette, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2006-00362-y 53, 233 (2006). (Pubitemid 44581774)
24. A. Arenas, A. Díaz-Guilera, and C. J. Pérez-Vicente, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.96.114102 96, 114102 (2006).
25. A. Arenas, A. Fernandez, and S. Gomez, Handb. Biol. Networks 1793-1037 10.1142/9789812838803-0011 10, 243 (2009).
26. P. H. A. Sneath and R. R. Sokal, Numerical Taxonomy (W. H. Freeman, San Francisco, 1973).
27. L. Zemanová, C. Zhou, and J. Kurths, Phys. D 0167-2789 10.1016/j.physd.2006.09.008 224, 202 (2006). (Pubitemid 44751202)
28. C. Zhou, L. Zemanová, G. Zamora, C. C. Hilgetag, and J. Kurths, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.238103 97, 238103 (2006). (Pubitemid 44888105)
29. The cortical area that is not a superhub is a border area that can be seen as a hub only joined with another one very similar to it but is regarded as a superhub in itself anyway.
30. J. L. Rodgers and W. A. Nicewander, Am. Stat. ASTAAJ 0003-1305 10.2307/2685263 42, 59 (1988).
31. R. Sharan, I. Ulitsky, and R. Shamir, Mol. Syst. Biol. 1744-4292 10.1038/msb4100129 3, 88 (2007). (Pubitemid 46423534)
32. S. C. Janga, J. J. Díaz-Mejía, and G. Moreno-Hagelsieb, Metab. Eng. 1096-7176 10.1016/j.ymben.2010.07.001 13, 1 (2011).
33. S. Fortunato and M. Barthelemy, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.0605965104 104, 36 (2007). (Pubitemid 46075032)
34. J. W. Scannell, G. A. P. C. Burns, C. C. Hilgetag, M. A. O'Neil, and M. P. Young, Cereb. Cortex 53OPAV 1047-3211 10.1093/cercor/9.3.277 9, 277 (1999). (Pubitemid 29231233)
35. M. Timme, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.224101 98, 224101 (2007). (Pubitemid 47139748)
36. J. Tegner, M. K. S. Yeung, J. Hasty, and J. Collins, Proc. Natl. Acad. Sci. USA 0027-8424 10.1073/pnas.0933416100 100, 5944 (2003). (Pubitemid 36576912)
37. D. di Bernardo, M. Thompson, T. Gardner, S. Chobot, E. Eastwood, A. Wojtovich, S. Elliott, S. Schaus, and J. Collins, Nat. Biotechnol. 1087-0156 10.1038/nbt1075 23, 377 (2005). (Pubitemid 41094431)
38. S. Gorur Shandilya and M. Timme, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/13/1/013004 13, 013004 (2011).
39. A. Díaz-Guilera and A. Arenas, in Bio-Inspired Computing and Communication, Lecture Notes in Computer Science Vol. 5151, edited by, P. Liò, E. Yoneki, J. Crowcroft, and, D. C. Verma, (Springer, Berlin Heidelberg, 2008), pp. 184-191.