Synchronization in an array of chaotic systems coupled via a directed graph

Proceedings - IEEE International Symposium on Circuits and Systems

Volumn , Issue , 2005, Pages 6046-6049

  Wu, Chai Wah ^a  

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

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRAIC CONNECTIVITY; ANALYTICAL RESULTS; COOPERATIVE COUPLING; COUPLED CHAOTIC SYSTEM; COUPLING MATRIX; DIRECTED GRAPHS; DIRECTED TREES; NONRECIPROCAL; SUFFICIENT CONDITIONS; UNDIRECTED GRAPH; WEIGHTED DIRECTED GRAPH;

DECISION TREES; GRAPH THEORY; SYNCHRONIZATION;

CHAOTIC SYSTEMS;

EID: 24944589849     PISSN: 02714310     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISCAS.2005.1466018     Document Type: Conference Paper

References (19)

1. C. W. Wu and L. O. Chua, "Synchronization in an array of linearly coupled dynamical systems," IEEE Trans. on Circ. and Syst.-I, vol. 42, no. 8, pp. 430-447, 1995.
2. C. W. Wu, Synchronization in coupled chaotic circuits and systems. World Scientific, 2002.
3. X. F. Wang and G. Chen, "Synchronization in small-world dynamical networks," Int. J. of Bif. and Chaos, vol. 12, no. 1, pp. 187-192, 2002.
4. 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.
5. L. O. Chua and D. N. Green, "Graph-theoretical properties of dynamic nonlinear networks," Tech. Rep. Memo ERL-M507, College of Engineering, University of California, Berkeley, 1975.
6. C. W. Wu and L. O. Chua, "Application of Kronecker products to the analysis of systems with uniform linear coupling," IEEE Trans. on Circ. and Syst.-I, vol. 42, no. 10, pp. 775-778, 1995.
7. C. W. Wu, "Perturbation of coupling matrices and its effect on the synchronizability in arrays of coupled chaotic circuits," Physics Letters A, vol. 319, pp. 495-503, 2003.
8. C. W.Wu, "Synchronization in networks of nonlinear dynamical systems coupled via a directed graph," Nonlinearity, in press.
9. M. Fiedler, "Algebraic connectivity of graphs," Czechoslovak Mathematical Journal, vol. 23, no. 98, pp. 298-305, 1973.
10. B. Mohar, "Some applications of Laplace eigenvalues of graphs," in Graph Symmetry: Algebraic Methods and Applications (G. Hahn and G. Sabidussi, eds.), pp. 225-275, Kluwer, 1997.
11. R. A. Brualdi and H. J. Ryser, Combinatorial Matrix Theory. Cambridge University Press, 1991.
12. C. W. Wu, "Algebraic connectivity of directed graphs," Linear and Multilinear Algebra, in press.
13. C. W. Wu, "On Rayleigh-Ritz ratios of a generalized Laplacian matrix of directed graphs," Linear Algebra and Its Applications, in press.
14. C. W. Wu, "On bounds of extremal eigenvalues of irreducible and m-reducible matrices," Linear Algebra and Its Applications, in press.
15. C. W. Wu, "Synchronization in systems coupled via complex networks," in Proceedings of IEEE ISCAS 2004, pp. IV-724-727, 2004.
16. C. W. Wu, "On a matrix inequality and its application to the synchronization in coupled chaotic systems," IBM Research Report RC23155, 2004, submitted for publication.
17. L. M. Pecora and T. L. Carroll, "Master stability functions for synchronized chaos in arrays of oscillators," in Proceedings of the 1998 IEEE Int. Symp. Circ. Syst., vol. 4, pp. IV-562-567, IEEE, 1998.
18. C. W. Wu, "Synchronization in arrays of coupled nonlinear systems with delay and nonreciprocal time-varying coupling," IEEE Trans. Circuits and Systems-II, in press.
19. M. Vidyasagar, Nonlinear Systems Analysis, 2nd Ed., Prentice-Hall, 1993.