Synchronization in Arrays of Coupled Nonlinear Systems With Delay and Nonreciprocal Time-Varying Coupling

IEEE Transactions on Circuits and Systems II: Express Briefs

Volumn 52, Issue 5, 2005, Pages 282-286

  Wu, Chai Wah ^a  

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

Author keywords

Delay systems; directed graphs; Lyapunov methods; nonlinear systems; synchronization

Indexed keywords

ARRAYS; DELAY CONTROL SYSTEMS; LYAPUNOV METHODS; MATRIX ALGEBRA; SYNCHRONIZATION; THEOREM PROVING; TIME VARYING CONTROL SYSTEMS; VECTORS;

COUPLED NONLINEAR SYSTEMS; DELAY SYSTEMS; DIRECTED GRAPHS; TIME VARYING COUPLING;

NONLINEAR CONTROL SYSTEMS;

EID: 20444387888     PISSN: 15497747     EISSN: 15583791     Source Type: Journal    
DOI: 10.1109/TCSII.2005.846884     Document Type: Article

References (18)

1. 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.
2. C. W. Wu, Synchronization in Coupled Chaotic Circuits and Systems. Singapore: World Scientific, 2002.
3. C. W. Wu and L. O. Chua, “Synchronization in coupled arrays of chaotic oscillators with nonreciprocal coupling,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 2, pp. 294–297, Feb. 2003.
4. C. W. Wu and L. O. Chua, “Perturbation of coupling matrices and its effect on the synchronizability in arrays of coupled chaotic circuits,” Phys. Lett. A, vol. 319, pp. 495–503, 2003.
5. V. N. Belykh, I. V. Belykh, and M. Hasler, “Connection graph stability method for synchronized coupled chaotic systems,” Phys. D, vol. 195, pp. 159–187, 2004.
6. J. Lii, X. Yu, and G. Chen, “Chaos synchronization of general complex dynamical systems,” Phys. A, vol. 334, pp. 281–302, 2004.
7. M. Amano, Z.-W. Luo, and S. Hosoe, “Graph dependant sufficient conditions for synchronization of dynamic network system with time-delay,” in Proc. 4th IFAC Workshop on Time Delay Systems (TDS'03), 2003.
8. M. Earl and S. Strogatz, “Synchronization in oscillator networks with delayed coupling: A stability criterion,” Phys. Rev. E, vol. 67, p. 036 204, 2003.
9. C. W. Wu, “Synchronization in arrays of chaotic circuits coupled via hypergraphs: Static and dynamic coupling,” in Proc. IEEE Int. Symp. Circuits Systems, vol. 3, 1998, pp. 287–290.
10. J. K. Hale, Theory of Functional Differential Equations. New York: Springer-Verlag, 1977.
11. V. Lakshmikantham and X. Z. Liu, Stability Analysis in Terms of Two Measures. Singapore: World Scientific, 1993.
12. C. W. Wu and L. O. Chua, “A unified framework for synchronization and control of dynamical systems,” Int. J. Bifurc. Chaos, vol. 4, no. 4, pp. 979–998, 1994.
13. L. O. Chua and D. N. Green, “Graph-theoretical properties of dynamic nonlinear networks,” College of Eng., Univ.of California, Berkeley, CA, Tech. Rep. Memo ERL-M507, 1975.
14. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1985.
15. C. W. Wu, “On Rayleigh-Ritz ratios of a generalized Laplacian matrix of directed graphs,” Linear Alg. Appl., to be published.
16. C. W. Wu, “Algebraic connectivity of directed graphs,” Linear Multinlear Alg., to be published.
17. M. Fiedler, “Algebraic connectivity of graphs,” Czech. Math. J., vol. 23, no. 98, pp. 298–305, 1973.
18. C. W. Wu and L. O. Chua, “Application of graph theory to the synchronization in an array of coupled nonlinear oscillators,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 42, no. 8, pp. 494–497, Aug. 1995.