Synchronizability of networks of chaotic systems coupled via a graph with a prescribed degree sequence

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 346, Issue 4, 2005, Pages 281-287

  Wu, Chai Wah ^a  

^a IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

Eigenvalue analysis; Nonlinear dynamics; Random graphs; Scale free networks; Synchronization

Indexed keywords

CHAOTIC SYSTEMS; COMPLEX NETWORKS; DYNAMICS; EIGENVALUES AND EIGENFUNCTIONS; GRAPH THEORY;

CONNECTED GRAPH; DEGREE SEQUENCE; EIGENVALUE ANALYSIS; PRESCRIBED DEGREE SEQUENCE; RANDOM GRAPHS; RANDOM NETWORK MODELS; SYNCHRONIZABILITY;

SYNCHRONIZATION;

EID: 24944539632     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2005.07.089     Document Type: Article

References (34)

1. C.W. Wu, and L.O. Chua IEEE Trans. Circuits Syst. I 42 8 1995 430
2. C.W. Wu, and L.O. Chua IEEE Trans. Circuits Syst. I 42 8 1995 494
3. L.M. Pecora, and T.L. Carroll Master stability functions for synchronized chaos in arrays of oscillators Proceedings of the IEEE International Symposium on Circuits and Systems vol. 4 1998 IV-562 IV-567
4. M. Barahona, and L.M. Pecora Phys. Rev. Lett. 89 5 2002 054101
5. C.W. Wu Global synchronization in coupled map lattices Proceedings of the IEEE International Symposium on Circuits and Systems vol. 3 1998 III-302 III-305
6. C.W. Wu Synchronization in Coupled Chaotic Circuits and Systems 2002 World Scientific
7. A. Jadbabaie, J. Lin, and A.S. Morse IEEE Trans. Automatic Control 48 6 2003 988
8. L. Mureau, Leaderless coordination via bidirectional and unidirectional time-dependent communication, preprint
9. R. Olfati-Saber, and R.M. Murray IEEE Trans. Automatic Control 49 9 2004 1520
10. Y. Hatano, and M. Mesbahi Agreement over random networks Proceedings of the 43rd IEEE Conference on Decision and Control 2004 2010 2015
11. C.W. Wu IEEE Trans. Circuits Syst. I 50 2 2003 294
12. C.W. Wu Linear Multilinear Algebra 53 3 2005 203
13. C.W. Wu Linear Algebra Appl. 402 2005 207
14. C.W. Wu Nonlinearity 18 2005 1057
15. C.W. Wu Synchronization in an array of chaotic systems coupled via a directed graph Proceedings of the IEEE International Symposium on Circuits and Systems 2005 6046 6049
16. C.W. Wu IEEE Trans. Circuits Syst. II 53 5 2005 282
17. M. Fiedler Czechoslovak Math. J. 23 98 1973 298
18. B. Mohar The Laplacian spectrum of graphs Y. Alavi G. Chartrand O.R. Oellermann A.J. Schwenk Graph Theory, Combinatorics, and Applications vol. 2 1991 Wiley 871 898
19. R. Merris Linear Algebra Appl. 197-198 1994 143
20. B. Mohar Some applications of Laplace eigenvalues of graphs G. Hahn G. Sabidussi Graph Symmetry: Algebraic Methods and Applications 1997 Kluwer Academic Publishers 225 275
21. M.E.J. Newman SIAM Rev. 45 2 2003 167
22. B. Bollobás Random Graphs second ed. 2001 Cambridge Univ. Press
23. T. Nishikawa, A.E. Motter, Y.-C. Lai, and F.C. Hoppensteadt Phys. Rev. Lett. 91 1 2003 014101
24. C.W. Wu Synchronization in arrays of coupled nonlinear systems: passivity, circle criterion and observer design Proceedings of IEEE International Symposium on Circuits and Systems vol. 3 2001 III-692 III-695
25. C.W. Wu Phys. Lett. A 319 2003 495
26. C.W. Wu Synchronization in systems coupled via complex networks Proceedings of the IEEE International Symposium on Circuits and Systems vol. 4 2004 IV-724 IV-727
27. F.M. Atay, T. Biyikoǧlu, J. Jost, On the synchronization of networks with prescribed degree distributions, Technical report, Max Planck Institute for Mathematics in the Sciences, nlin/0407024
28. B. Bollobás Modern Graph Theory Graduate Texts in Mathematics vol. 184 1998 Springer
29. P. Erdös, and T. Gallai Mat. Lapok 11 1960 264
30. G. Sierksma, and H. Hoogeveen J. Graph Theory 15 2 1991 223
31. J. Friedman, J. Kahn, and E. Szemerédi On the second eigenvalue in random regular graphs Proceedings of the 21st Annual ACM Symposium on Theory of Computing 1989 587 598
32. V. Havel Casopis Pest. Mat. 80 1955 477
33. S.L. Hakimi SIAM J. Appl. Math. 10 1962 496
34. F. Juhász Discrete Math. 96 1991 59