Global synchronization of discrete-time dynamical network with a directed graph

IEEE Transactions on Circuits and Systems II: Express Briefs

Volumn 54, Issue 2, 2007, Pages 136-140

  Lu, Wenlian ^a,b   Chen, Tianping ^b  

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

^b FUDAN UNIVERSITY   (China)

Author keywords

Diagonally stable; directed graph; linearly coupled map lattices (LCMLs); spanning tree; synchronization

Indexed keywords

CHAOS THEORY; GRAPH THEORY; SYNCHRONIZATION; TOPOLOGY; TREES (MATHEMATICS);

DISCRETE-TIME DYNAMICAL NETWORK; LINEARLY COUPLED MAP LATTICES (LCMLS); SPANNING TREE;

DISCRETE TIME CONTROL SYSTEMS;

EID: 33947580864     PISSN: 15497747     EISSN: 15583791     Source Type: Journal    
DOI: 10.1109/TCSII.2006.886236     Document Type: Article

References (25)

1. T. Bohr and O. B. Christensen, “Size dependence, coherence, and scaling in turbulent coupled map lattices,” Phys. Rev. Lett., vol. 63, pp. 2161–2164, 1989.
2. K. Kaneko, Theory and Applications of Coupled Map Lattices. New York: Wiley, 1993.
3. Y. Jiang and P. Parmananda, “Synchronization of spatiotemporal chaos in asymmetrically coupled map lattices,” Phys. Rev. E, vol. 57, no. 4, pp. 4135–4139, 1998.
4. P. M. Gade and C.-K. Hu, “Synchronous chaos in coupled map lattices,” Phys. Rev. E, vol. 65, no. 5, pp. 6409–6413, 2000.
5. J. Jost and M. P. Joy, “Spetral properties and synchronization in coupled map lattices,” Phys. Rev. E, vol. 65, p. 016201, 2001.
6. J. Jost, Dynamical Networks preprinted, 2005.
7. G. Rangarajan and M. Ding, “Stability of synchronized chaos in coupled dynamical systems,” Phys. Lett. A, vol. 296, pp. 204–209, 2002.
8. Y. H. Chen, G. Rangarajan, and M. Ding, “General stability analysis of synchronized dynamics in coupled systems,” Phys. Rev. E., vol. 67, p. 026209, 2003.
9. F. Atay and J. Jost, “On the emergence of complex systems on the basis of the coordination of complex behaviors of their elements: Synchronization and complexity,” Complexity, vol. 10, pp. 17–22, 2004.
10. W. Lu and T. Chen, “Synchronization analysis of linearly coupled networks of discrete time systems,” Physica D, vol. 198, pp. 148–168, 2004.
11. R. E. Amritkar, S. Jalan, and C.-K. Hu, “Synchronization clusters in coupled map networks. II. Stability analysis,” Phys. Rev. E, vol. 72, p. 016212, 2005.
12. H. Atmanspacher, T. Filk, and H. Scheingraber, “Stability analysis of coupled map lattices at locally unstable fixed points,” Eur. Phys. J. Biol., vol. 44, pp. 229–239, 2004.
13. C. W. Wu and L. O. Chua, “Synchronization in an array of linearly coupled dynamical systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 42, no. 8, pp. 430–447, Aug. 1995.
14. V. N. Belykh, I. V. Belykh, and M. Hasler, “Connection graph stability method for synchronized coupled chaotic systems,” Physica D, vol. 195, pp. 159–187, 2004.
15. C. W. Wu, “Synchronization in networks of nonlinear dynamical systems coupled via a directed graph,” Nonlinearity, vol. 18, pp. 1057–1064, 2005.
16. F. Chung, L. Lu, and V. Vu, “The spectral of random graph with given expected degrees,” in Proc. Nat. Acad. Sci., 2003, vol. 100, no. 11, pp. 6313–6318.
17. A. Bhaya and E. Kaszkurewicz, “On discrete-time diagonal and D-stable,” Linear Alg. Appl., vol. 187, pp. 87–104, 1993.
18. C. Godsil and G. Royle, Algebraic Graph Theory. New York: Springer-Verlag, 2001.
19. A. Berman, Completely Positive Matrices. Singapore: World Scientific, 2003.
20. M. Araki, “Applications of M-matrices to the stability problems of composite dynamical systems,” J. Math. Anal. Appl., vol. 52, pp. 309–321, 1975.
21. F. M. Atay, T. Biyikoglu, and J. Jost, “Synchronization of networks with prescribed degree distribution,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 53, no. 1, pp. 92–98, Jan. 2006.
22. C. W. Wu, “Algebraic connectivity of directed graphs,” Linear Multilinear Algebra, vol. 53, no. 3, pp. 203–223, 2005.
23. C. W. Wu, “On Rayleigh-Ritz ratios of a generalized Laplacian matrix of directed graphs,” Linear Algebra Appl., vol. 402, pp. 207–227, 2005.
24. M. Fiedler, “Algebraic connectivity of graphs,” Czech. Math. J., vol. 23, no. 98, pp. 298–305, 1973.
25. Z. Li and G. Chen, “Global synchronization and asymptotic stability of complex dynamical networks,” IEEE Trans. Circuits Syst. II: Exp. Briefs, vol. 53, no. 1, pp. 28–33, Jan. 2006.