Network synchronization: Spectral versus statistical properties

Physica D: Nonlinear Phenomena

Volumn 224, Issue 1-2, 2006, Pages 35-41

  Atay, Fatihcan M ^a   Biyikoǧlu, Türker ^b,c   Jost, Jürgen ^a  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^c ISIK UNIVERSITY   (Turkey)

Author keywords

Algebraic connectivity; Degree distribution; Graph; Laplacian; Synchronization

Indexed keywords

CORRELATION METHODS; EIGENVALUES AND EIGENFUNCTIONS; GRAPH THEORY; NONLINEAR SYSTEMS; SYNCHRONIZATION;

ALGEBRAIC CONNECTIVITY; DEGREE DISTRIBUTION; GRAPHS; LAPLACIAN;

COMPUTER NETWORKS;

EID: 33750991862     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2006.09.018     Document Type: Article

References (34)

1. Albert R., and Barabási A.-L. Statistical mechanics of complex networks. Rev. Modern Phys. 74 (2002) 47-97
2. S.N. Dorogovtsev, J.F.F. Mendes, Evolution of Networks, Oxford, 2003
3. Newman M.E.J. The structure and function of complex networks. SIAM Rev. 45 2 (2003) 167-256
4. Barabási A.-L., and Albert R.A. Emergence of scaling in random networks. Science 286 (1999) 509-512
5. Pecora L.M., and Carroll T.L. Synchronization in chaotic systems. Phys. Rev. Lett. 64 (1990) 821-824
6. Pecora L.M., and Carroll T.L. Master stability functions for synchronized coupled systems. Phys. Rev. Lett. 80 10 (1998) 2109-2112
7. Jost J., and Joy M.P. Spectral properties and synchronization in coupled map lattices. Phys. Rev. E 65 (2002) 016201
8. Li X., and Chen G. Synchronization and desynchronization of complex dynamical networks: An engineering viewpoint. IEEE Trans. Circuits Syst. I 50 11 (2003) 1381-1390
9. Nishikawa T., Motter A.E., Lai Y.-C., and Hoppensteadt F.C. Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?. Phys. Rev. Lett. 91 (2003) 014101
10. Motter A.E., Zhou C., and Kurths J. Enhancing complex-network synchronization. Europhys. Lett. 69 (2005) 334
11. Motter A.E., Zhou C., and Kurths J. Network synchronization, diffusion, and the paradox of heterogeneity. Phys. Rev. E 71 (2005) 016116
12. Wu X., Wang B., Zhou T., Wang W., Zhao M., and Yang H. Synchronizability of highly clustered scale-free networks. Chinese Phys. Lett. 23 4 (2006) 1046-1049
13. di Bernardo M., Garofalo F., and Sorrentino F. Synchronizability of degree correlated networks. cond-mat/0504335
14. Hong H., Kim B.J., Choi M.Y., and Park H. Factors that predict better synchronizability on complex networks. Phys. Rev. E 65 (2002) 067105
15. Barahona M., and Pecora L.M. Synchronization in small-world systems. Phys. Rev. Lett. 89 5 (2002) 054101
16. Hong H., Choi M.Y., and Kim B.J. Synchronization on small-world networks. Phys. Rev. E 69 (2004) 026139
17. Mohar B. Graph Laplacians. Topics in Algebraic Graph Theory (2004), Cambridge University Press, Cambridge 113-136
18. Atay F.M., and Bi{dotless}yi{dotless}koǧlu T. Graph operations and synchronization of complex networks. Phys. Rev. E 72 (2005) 016217
19. Pikovsky A., Rosenblum M., and Kurths J. Synchronization-A Universal Concept in Nonlinear Science (2001), Cambridge University Press, Cambridge
20. In: Kaneko K. (Ed). Theory and Applications of Coupled map Lattices (1993), Wiley, New York
21. W. Lu, F.M. Atay, J. Jost, Synchronization of discrete-time dynamical networks with time-varying couplings (submitted for publication)
22. Atay F.M., Jost J., and Wende A. Delays, connection topology, and synchronization of coupled chaotic maps. Phys. Rev. Lett. 92 14 (2004) 144101
23. Atay F.M., and Jost J. On the emergence of complex systems on the basis of the coordination of complex behaviors of their elements: Synchronization and complexity. Complexity 10 1 (2004) 17-22
24. Lu W., and Chen T. Synchronization analysis of linearly coupled networks of discrete time systems. Physica D 198 (2004) 148-168
25. Pecora L.M., and Barahona M. Synchronization of oscillators in complex networks. Chaos Complexity Lett. 1 (2005) 61-91
26. Mohar B. Isoperimetric numbers of graphs. J. Combin. Theory Ser. B 47 3 (1989) 274-291
27. Belykh V.N., Belykh I.V., and Hasler M. Connection graph stability method for synchronized coupled chaotic systems. Physica D 195 1-2 (2004) 159-187
28. Stilwell D.J., Bollt E.M., and Roberson D.G. Sufficient conditions for fast switching synchronization in time-varying network topologies. SIAM J. Appl. Dyn. Syst. 5 1 (2006) 140-156 (electronic)
29. Atay F.M., Bi{dotless}yi{dotless}koǧlu T., and Jost J. Synchronization of networks with prescribed degree distributions. IEEE Trans. Circuits Syst. I 53 1 (2006) 92-98
30. Edmonds J. Existence of k-edge connected ordinary graphs with prescribed degrees. J. Res. Natl Bur. Stand. Sect. B 68B (1964) 73-74
31. Watts D.J., and Strogatz S.H. Collective dynamics of 'small-world' networks. Nature 393 (1998) 440-442
32. Wu C.W. Synchronization in networks of nonlinear dynamical systems coupled via a directed graph. Nonlinearity 18 (2005) 1057-1064
33. Kocarev L., and Amato P. Synchronization in power-law networks. Chaos 15 2 (2005) 024101
34. Chung F., Lu L., and Vu V. Spectra of random graphs with given expected degrees. Proc. Natl Acad. Sci. USA 100 11 (2003) 6313-6318 (electronic)