Synchronization of chaotic systems with time-varying coupling delays

Tingwen Huang; Guanrong Chen; Juergen Kurths

doi:10.3934/dcdsb.2011.16.1071

Article Contents

2011, Volume 16, Issue 4: 1071-1082. Doi: 10.3934/dcdsb.2011.16.1071

This issue Previous Article Three-dimensional cerebrospinal fluid flow within the human central nervous system Next Article Perturbation solution of the coupled Stokes-Darcy problem

Synchronization of chaotic systems with time-varying coupling delays

1.
Texas A&M University at Qatar, Doha, P.O.Box 23874
2.
Department of Electronic Engineering, City University of Hong Kong, Hong Kong
3.
Institute for Physics, University of Potsdam, Am Neuen Palais, Gebude 19, D-14415 Potsdam

Received: October 2010

Revised: May 2011

Published: June 2011

Abstract Related Papers Cited by

Abstract

In this paper, we study the complete synchronization of a class of time-varying delayed coupled chaotic systems using feedback control. In terms of Linear Matrix Inequalities, a sufficient condition is obtained through using a Lyapunov-Krasovskii functional and differential equation inequalities. The conditions can be easily verified and implemented. We present two simulation examples to illustrate the effectiveness of the proposed method.

Keywords:

Mathematics Subject Classification: Primary: 34A20, 34G20.

Citation:

Related Papers

Cited by

References

[1]	S. Boccaletti, J. Kurths, G. Osipov, D. L. Vallares and C. S. Zhou, The synchronization of chaotic systems, Phys. Rep., 366 (2002), 1-101.doi: 10.1016/S0370-1573(02)00137-0.
[2]	S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, "Linear Matrix Inequalities In Systems And Control Theory," SIAM Studies in Applied Mathematics, 15, SIAM, Philadephia, PA, 1994.
[3]	J. Cao and J. Lu, Adaptive synchronization of neural networks with or without time-varying delay, Chaos, 16 (2006), 013133, 6 pp.
[4]	P. Colet and R. Roy, Digital communication with synchronized chaotic lasers, Opt. Lett., 19 (1994), 2056.doi: 10.1364/OL.19.002056.
[5]	K. Gopalsamy, "Stability and Oscillations in Delay Differential Equations of Population Dynamics," Mathematics and its Applications, 74, Kluwer Academic Publishers Group, Dordrecht, 1992.
[6]	H. G. Schuster, ed., "Handbook of Chaos Control: Foundations and Applications," Wiley-VCH, Weinheim, 1999.
[7]	H. Huang, G. Feng and Y. Sun, Robust synchronization of chaotic systems subject to parameter uncertainties, Chaos, 19 (2009), 033128.doi: 10.1063/1.3212940.
[8]	T. Huang, C. Li and X. Liu, Synchronization of chaotic systems with delay using intermittent linear state feedback, Chaos, 18 (2008), 033122, 8 pp.
[9]	C. Li, G. Feng and X. Liao, Stabilization of nonlinear systems via periodically intermittent control, IEEE Trans. Circuits and Systems II, 54 (2006), 1019-1023.
[10]	C. Li, X. Liao and K. Wong, Chaotic lag synchronization of coupled time-delayed systems and its application in secure communication, Physica D, 194 (2004), 187-202.doi: 10.1016/j.physd.2004.02.005.
[11]	X. Liu, T. Chen and W. Lu, Cluster synchronization for linearly coupled complex networks, Journal of Industrial and Management Optimization (JIMO), 7 (2011), 87-101.doi: 10.3934/jimo.2011.7.87.
[12]	J. Lu, J. Cao and D. Ho, Adaptive stabilization and synchronization for chaotic lur’e systems with time-varying delay, IEEE Transactions on Circuits and Systems I: Regular Papers, 55 (2008), 1347-1356.doi: 10.1109/TCSI.2008.916462.
[13]	L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett., 64 (1990), 821-824.doi: 10.1103/PhysRevLett.64.821.
[14]	J. Qing, Projective synchronization of a new hyperchaotic Lorenz system, Physics Letters A, 370 (2007), 40-45.doi: 10.1016/j.physleta.2007.05.028.
[15]	F. Rogister, D. Pieroux, M. Sciamanna, P. Megret and M. Blondel, Anticipating synchronization of two chaotic laser diodes by incoherent optical coupling and its application to secure communications, Optics Communications, 207 (2002), 295-306.doi: 10.1016/S0030-4018(02)01494-3.
[16]	M. Rosenblum and A. Pikovsky, Phase synchronization of chaotic oscillators, Phys. Rev. Lett., 76 (1996), 1804-1807.doi: 10.1103/PhysRevLett.76.1804.
[17]	N. Rulkov and M. Sushchik, Generalized synchronization of chaos in directionally coupled chaotic systems, Phys. Rev. E, 51 (1995), 980-994.doi: 10.1103/PhysRevE.51.980.
[18]	S. Sivaprakasam and P. Spencer, Regimes of chaotic synchronization in external-cavity laser diodes, IEEE Journal of Quantum Electronics, 38 (2002), 1155-1161.doi: 10.1109/JQE.2002.801949.
[19]	Q. Song and J. Cao, Global dissipativity analysis on uncertain neural networks with mixed time-varying delays, Chaos, 18 (2008), 043126, 10 pp.
[20]	K. Thornburg, M. Moller, R. Roy and T. Carr, Chaos and coherence in coupled lasers, Phys. Rev. E, 55 (1997), 3865.doi: 10.1103/PhysRevE.55.3865.
[21]	J. Wang, Z. Yang, T. Huang and M. Xiao, Local and global exponential synchronization of complex delayed dynamical networks with general topology, Discrete and Continuous Dynamical Systems-Series B, 16 (2011), 393-408.doi: 10.3934/dcdsb.2011.16.393.
[22]	R. Zhen, X. Wu and J. Zhang, "Sliding Model Synchronization Controller Design for Chaotic Neural Network with Time-Varying Delay," Proceedings of the 8th World Congress on Intelligent Control and Automation, China, (2010), 3914-3919.doi: 10.1109/WCICA.2010.5554977.