Multiple effects of gradient coupling on network synchronization

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

Volumn 77, Issue 5, 2008, Pages

  Wang, Xingang ^a   Zhou, Cangtao ^b   Lai, Choy Heng ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b INSTITUTE OF APPLIED PHYSICS AND COMPUTATIONAL MATHEMATICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; GRADIENT METHODS; SYNCHRONIZATION;

GRADIENT COUPLING; SYNCHRONIZABILITY;

LARGE SCALE SYSTEMS;

EID: 43949110998     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.77.056208     Document Type: Article

References (23)

1. D. J. Watts and S. H. Strogatz, Nature (London) NATUAS 0028-0836 10.1038/30918 393, 440 (1998).
2. A.-L. Barabási and R. Albert, Science SCIEAS 0036-8075 10.1126/science.286.5439.509 286, 509 (1999).
3. S. H. Strogatz, Nature (London) NATUAS 0028-0836 10.1038/35065725 410, 268 (2001).
4. R. Albert and A.-L. Barabási, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.47 74, 47 (2002).
5. M. E. J. Newman, SIAM Rev. SIREAD 0036-1445 10.1137/S003614450342480 45, 167 (2003).
6. S. Strogatz, Sync: The Emerging Science of Spontaneous Order (Hyperion, New York, 2003).
7. X. F. Wang and G. Chen, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127402004292 12, 187 (2002).
8. M. Barahona and L. M. Pecora, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.054101 89, 054101 (2002).
9. T. Nishikawa, A. E. Motter, Y.-C. Lai, and F. C. Hoppensteadt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.014101 91, 014101 (2003).
10. A. E. Motter, C. S. Zhou, and J. Kurths, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2004-10365-4 69, 334 (2005)
11. A. E. Motter, C. S. Zhou, and J. Kurths, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.016116 71, 016116 (2005).
12. D.-U. Hwang, M. Chavez, A. Amann, and S. Boccaletti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.138701 94, 138701 (2005).
13. M. Chavez, D.-U. Hwang, A. Amann, H. G. E. Hentschel, and S. Boccaletti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.218701 94, 218701 (2005).
14. T. Nishikawa and A. E. Motter, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.065106 73, 065106 (R) (2006)
15. T. Nishikawa and A. E. Motter, Physica D PDNPDT 0167-2789 10.1016/j.physd.2006.09.007 224, 77 (2006).
16. A. E. Motter, C. S. Zhou, and J. Kurths, AIP Conf. Proc. APCPCS 0094-243X 10.1063/1.1985389 776, 201 (2005).
17. M. Zhao, T. Zhou, B.-H. Wang, Q. Ou, and J. Ren, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2006-00383-6 53, 375 (2006).
18. X. G. Wang, Y.-C. Lai, and C.-H. Lai, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.75.056205 75, 056205 (2007).
19. One minor difference is that the root in Ref. is a single node, while in Eq. 2 it consists of a pair of mutually coupled nodes. This difference, however, does not affect our general conclusions about the gradient effects, especially when large-size networks are considered.
20. S. N. Dorogovtsev and J. F. F. Mendes, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730110112519 51, 1079 (2002).
21. Breaking phenomenon is also found in other types of complex networks such as the modular and assortative networks, there the breaking probability is also determined by other network parameters such as modularity and assortativity.
22. Numerically we find that βo is insensitive to γ. This can be heuristically understood as a competing result between the breaking probability and the total gradient strength. Under the same value of β, heterogeneous networks have small breaking probability but possess large gradient, the former enhances synchronization while the latter in general suppresses synchronization.
23. X. G. Wang, S. G. Guan, and C.-H. Lai (preprint).