Synchronization in symmetric bipolar population networks

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

Volumn 80, Issue 6, 2009, Pages

  Buzna, Lubos ^a,b   Lozano, Sergi ^a   Díaz Guilera, Albert ^a,c,d,e  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF ILINA   (Slovakia)

^c POTSDAM INSTITUTE FOR CLIMATE IMPACT RESEARCH   (Germany)

^d Ctr for Dynamics of Complex Systems   (Germany)

^e UNIVERSITY OF BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL ESTIMATIONS; COUPLING STRENGTHS; MINIMUM VALUE; NUMERICAL SIMULATION; PARTICULAR DISTRIBUTION; RANDOM TOPOLOGY; SYNCHRONIZATION DYNAMICS; THEORETICAL RESULT; TOPOLOGICAL LOCALIZATION;

COMPUTER SIMULATION; EVOLUTIONARY ALGORITHMS; NATURAL FREQUENCIES; SYNCHRONIZATION; TOPOLOGY;

FREQUENCY ESTIMATION;

EID: 75449120473     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.066120     Document Type: Article

References (31)

1. S. H. Strogatz, Nature (London) 410, 268 (2001). 10.1038/35065725
2. R. Albert and A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002). 10.1103/RevModPhys.74.47
3. S. Dorogovtsev and J. F. F. Mendes, Adv. Phys. 51, 1079 (2002). 10.1080/00018730110112519
4. M. E. J. Newman, SIAM Rev. 45, 167 (2003). 10.1137/S003614450342480
5. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, Phys. Rep. 424, 175 (2006). 10.1016/j.physrep.2005.10.009
6. L. da Fontoura Costa, F. A. Rodrigues, G. Travieso, and P. R. V. Boas, Adv. Phys. 56, 167 (2007). 10.1080/00018730601170527
7. M. E. J. Newman, Phys. Rev. Lett. 89, 208701 (2002). 10.1103/PhysRevLett. 89.208701
8. M. A. Serrano, M. Boguñá, R. Pastor-Satorras, and A. Vespignani, Structure and Dynamics of Complex Networks: From Information Technology to Finance and Natural Science (World Scientific, Singapore, 2007), pp. 35-66.
9. S. Zhou and R. J. Mondragon, IEEE Commun. Lett. 8, 180 (2004). 10.1109/LCOMM.2004.823426
10. M. Girvan and M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. 99, 7821 (2002). 10.1073/pnas.122653799
11. L. Danon, A. Díaz-Guilera, J. Duch, and A. Arenas, J. Stat. Mech. 9, 8 (2005).
12. A. Barrat, M. Barthelemy, and A. Vespignani, Dynamical Processes on Complex Networks (Cambridge University Press, Cambridge, 2008).
13. S. H. Strogatz, Sync: The Emerging Science of Spontaneous Order (Hyperion, New York, 2003).
14. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, New York, 1984).
15. J. A. Acebrón, L. L. Bonilla, C. J. Pérez-Vicente, F. Ritort, and R. Spigler, Rev. Mod. Phys. 77, 137 (2005). 10.1103/RevModPhys.77. 137
16. A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou, Phys. Rep. 469, 93 (2008). 10.1016/j.physrep.2008.09.002
17. M. Brede, Phys. Lett. A 372, 5305 (2008). 10.1016/j.physleta.2008.06.017
18. P. M. Gleiser and D. H. Zanette, Eur. Phys. J. B 53, 233 (2006). 10.1140/epjb/e2006-00362-y
19. E. A. Martens, E. Barreto, S. H. Strogatz, E. Ott, P. So, and T. M. Antonsen, Phys. Rev. E 79, 026204 (2009). 10.1103/PhysRevE.79.026204
20. E. Montbrió, D. Pazó, and J. Schmidt, Phys. Rev. E 74, 056201 (2006). 10.1103/PhysRevE.74.056201
21. L. L. Bonilla, C. J. Pérez Vicente, and R. Spigler, Physica D 113, 79 (1998). 10.1016/S0167-2789(97)00187-5
22. G. Filatrella, A. H. Nielsen, and N. F. Pedersen, Eur. Phys. J. B 61, 485 (2008). 10.1140/epjb/e2008-00098-8
23. J. A. Acebrón and R. Spigler, Phys. Rev. Lett. 81, 2229 (1998). 10.1103/PhysRevLett.81.2229
24. H. A. Tanaka, A. J. Lichtenberg, and S. Oishi, Phys. Rev. Lett. 78, 2104 (1997). 10.1103/PhysRevLett.78.2104
25. A. L. Barabási and R. Albert, Science 286, 509 (1999). 10.1126/science.286.5439.509
26. J. H. Kim and V. H. Vu, Proceedings of the 35th ACM Symposium on Theory of Computing (ACM Press, San Diego, 2003), pp. 213-222.
27. I. Sendiña-Nadal, J. Buldu, I. Leyva, and S. Boccaletti, PLoS ONE 3, e2644, (2008). 10.1371/journal.pone.0002644
28. J. Gómez-Gardeñes, Y. Moreno, and A. Arenas, Phys. Rev. Lett. 98, 034101 (2007). 10.1103/PhysRevLett.98.034101
29. M. Brede, Eur. Phys. J. B 62, 87 (2008). 10.1140/epjb/e2008-00126-9
30. A. Arenas, A. Díaz-Guilera, and C. J. Pérez-Vicente, Phys. Rev. Lett. 96, 114102 (2006). 10.1103/PhysRevLett.96.114102
31. The procedure can be enhanced, for instance, by applying a simulated annealing approach, where the rule deciding whether to accept or to reject the swap operation is probabilistic. Moreover, the initialization can speed up the maximization or minimization of network similarity when initial positions for each color (i.e. for each natural frequency) are chosen. For example, "flooding" the network with fitting colors starting from a selected node gives already close-to-optimal configurations.