Collection of master–slave synchronized chaotic systems

Abstract In this work the open-plus-closed-loop (OPCL) method of synchronization is used in order to synchronize the systems from the Sprott's collection of the simplest chaotic systems. The method is general and we looked for the simplest coupling between master and slave. The main result is that for the systems that contains one nonlinear term and that term contains one variable then the coupling consists of one term. The numerical intervals of parameters where the synchronization is achieved are obtained analytically by applying Routh–Hurwitz conditions. Detailed calculations and numerical results are given for the system I from the Sprott's collection. Working in the same manner for many systems this method can be adopted for the teaching of the topic.

[1]  J. Sprott,et al.  Some simple chaotic flows. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[3]  Yinping Zhang,et al.  Some simple global synchronization criterions for coupled time-varying chaotic systems , 2004 .

[4]  E. Atlee Jackson,et al.  An open-plus-closed-loop (OPCL) control of complex dynamic systems , 1995 .

[5]  Lilian Huang,et al.  Synchronization of chaotic systems via nonlinear control , 2004 .

[6]  Jitao Sun,et al.  Some global synchronization criteria for coupled delay-systems via unidirectional linear error feedback approach , 2004 .

[7]  Chun-Chieh Wang,et al.  A new adaptive variable structure control for chaotic synchronization and secure communication , 2004 .

[8]  M. K. Ali,et al.  Synchronization of chaos and hyperchaos using linear and nonlinear feedback functions , 1997 .

[9]  P. McClintock.  Synchronization:a universal concept in nonlinear science , 2003 .

[10]  Shihua Chen,et al.  A stable-manifold-based method for chaos control and synchronization , 2004 .

[11]  Shihua Chen,et al.  Synchronizing strict-feedback and general strict-feedback chaotic systems via a single controller , 2004 .

[12]  Chen Shi-Gang,et al.  GENERAL METHOD OF SYNCHRONIZATION , 1997 .

[13]  E. Mosekilde,et al.  Chaotic Synchronization: Applications to Living Systems , 2002 .

[14]  Li-Qun Chen,et al.  An Open-Plus-Closed-Loop Approach to Synchronization of Chaotic and hyperchaotic Maps , 2002, Int. J. Bifurc. Chaos.

[15]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

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