Global chaos synchronization with channel time-delay

Abstract This paper addresses a practical issue in chaos synchronization where there is a time-delay in the receiver as compared with the transmitter. A new synchronization scheme and a general criterion for global chaos synchronization are proposed and developed from the approach of unidirectional linear error feedback coupling with time-delay. The chaotic Chua’s circuit is used for illustration, where the coupling parameters are determined according to the criterion under which the global chaos synchronization of the time-delay coupled systems is achieved.

[1]  J. Suykens,et al.  Master-Slave Synchronization of Lur'e Systems , 1997 .

[2]  E. Bai,et al.  On the synchronization of a class of electronic circuits that exhibit chaos , 2002 .

[3]  Guanrong Chen,et al.  Generation of n-scroll attractors via sine function , 2001 .

[4]  Louis M. Pecora,et al.  Synchronizing chaotic circuits , 1991 .

[5]  Guanrong Chen,et al.  Generating chaos via x|x| , 2001 .

[6]  X. Shan,et al.  A linear feedback synchronization theorem for a class of chaotic systems , 2002 .

[7]  T. Kapitaniak,et al.  MONOTONE SYNCHRONIZATION OF CHAOS , 1996 .

[8]  Alan V. Oppenheim,et al.  Synchronization of Lorenz-based chaotic circuits with applications to communications , 1993 .

[9]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[10]  Maciej Ogorzalek,et al.  Taming chaos. I. Synchronization , 1993 .

[11]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[12]  Guanrong Chen,et al.  A simple global synchronization criterion for coupled chaotic systems , 2003 .

[13]  Jinhu Lu,et al.  Chaos synchronization between linearly coupled chaotic systems , 2002 .

[14]  Guanrong Chen,et al.  From Chaos To Order Methodologies, Perspectives and Applications , 1998 .

[15]  Leon O. Chua,et al.  Chaos Synchronization in Chua's Circuit , 1993, J. Circuits Syst. Comput..

[16]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[17]  H.F. Chen,et al.  Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation , 2000, IEEE Journal of Quantum Electronics.

[18]  J. P. Lasalle.  The stability of dynamical systems , 1976 .

[19]  Saverio Mascolo,et al.  SYNCHRONIZING HIGH DIMENSIONAL CHAOTIC SYSTEMS VIA EIGENVALUE PLACEMENT WITH APPLICATION TO CELLULAR NEURAL NETWORKS , 1999 .

[20]  O. Rössler.  An equation for continuous chaos , 1976 .

[21]  S. Mascolo,et al.  Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal , 1997 .

[22]  Akio Ushida,et al.  On synchronization phenomena in chaotic systems coupled by transmission line , 2000, 2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353).

[23]  A. A. Martyni︠u︡k.  Stability by Liapunov's matrix function method with applications , 1998 .

[24]  Moez Feki,et al.  Observer-based chaotic synchronization in the presence of unknown inputs , 2003 .

[25]  Johan A. K. Suykens,et al.  Master-Slave Synchronization of Lur'e Systems with Time-Delay , 2001, Int. J. Bifurc. Chaos.

[26]  L. Chua,et al.  The simplest dissipative nonautonomous chaotic circuit , 1994 .

[27]  Guo-Ping Jiang,et al.  A Global Synchronization Criterion for Coupled Chaotic Systems via Unidirectional Linear Error Feedback Approach , 2002, Int. J. Bifurc. Chaos.

[28]  L. Shilnikov.  CHUA’S CIRCUIT: RIGOROUS RESULTS AND FUTURE PROBLEMS , 1994 .

[29]  Teh-Lu Liao,et al.  Adaptive synchronization of chaotic systems and its application to secure communications , 2000 .