Coexistence of synchronization and anti-synchronization in the unified chaotic systems

This paper investigates the coexistence of anti-synchronization and synchronization in the unified chaotic systems. First, an algorithm is proposed to select what variables in the master system which can anti-synchronize the corresponding variables in the slave system. Then, several control strategy is presented to guarantee coexistence of synchronization and anti-synchronization in the unified chaotic system. Finally, numerical simulations verify the correctness and the effectiveness of the proposed results.

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

[2]  Rongwei Guo A simple adaptive controller for chaos and hyperchaos synchronization , 2008 .

[3]  Shihua Chen,et al.  Adaptive control for anti-synchronization of Chua's chaotic system , 2005 .

[4]  Rongwei Guo,et al.  Modification for collection of master–slave synchronized chaotic systems , 2009 .

[5]  Guangming Wang,et al.  Stabilization and synchronization of Genesio–Tesi system via single variable feedback controller , 2010 .

[6]  Suwat Kuntanapreeda,et al.  Chaos synchronization of unified chaotic systems via LMI , 2009 .

[7]  S. Bowong Stability analysis for the synchronization of chaotic systems with different order: application to secure communications , 2004 .

[8]  Chi-Bin Cheng,et al.  An asymmetric image cryptosystem based on the adaptive synchronization of an uncertain unified chaotic system and a cellular neural network , 2013, Commun. Nonlinear Sci. Numer. Simul..

[9]  Mohamed Benrejeb,et al.  Feedback control design for Rössler and Chen chaotic systems anti-synchronization , 2010 .

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

[11]  Debin Huang,et al.  A Simple Adaptive-feedback Controller for Identical Chaos Synchronization , 2022 .

[12]  Chongxin Liu,et al.  Passive control on a unified chaotic system , 2010 .

[13]  M. Mossa Al-sawalha,et al.  Adaptive anti-synchronization of chaotic systems with fully unknown parameters , 2010, Comput. Math. Appl..

[14]  Jinhu Lü,et al.  Coexistence of anti-phase and complete synchronization in the generalized Lorenz system , 2010 .

[15]  Guo Rong-Wei Simultaneous Synchronization and Anti-Synchronization of Two Identical New 4D Chaotic Systems , 2011 .

[16]  Hao Shen,et al.  Adaptive stabilization of uncertain unified chaotic systems with nonlinear input , 2011, Appl. Math. Comput..

[17]  Yinping Zhang,et al.  Chaotic synchronization and anti-synchronization based on suitable separation , 2004 .