Combination–combination synchronization among four identical or different chaotic systems

Based on one drive system and one response system synchronization model, a new type of combination–combination synchronization is proposed for four identical or different chaotic systems. According to the Lyapunov stability theorem and adaptive control, numerical simulations for four identical or different chaotic systems with different initial conditions are discussed to show the effectiveness of the proposed method. Synchronization about combination of two drive systems and combination of two response systems is the main contribution of this paper, which can be extended to three or more chaotic systems. A universal combination of drive systems and response systems model and a universal adaptive controller may be designed to our intelligent application by our synchronization design.

[1]  Luo Runzi,et al.  Active Backstepping-Based Combination Synchronization of Three Different Chaotic Systems , 2012 .

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

[3]  Parlitz,et al.  Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. , 1996, Physical review letters.

[4]  Xingyuan Wang,et al.  Projective synchronization of nonlinear-coupled spatiotemporal chaotic systems , 2010 .

[5]  Parlitz,et al.  Phase synchronization of coupled ginzburg-landau equations , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[7]  Meng Liu,et al.  Adaptive projective synchronization of dynamical networks with distributed time delays , 2012 .

[8]  Chunguang Li,et al.  Phase synchronization in small-world networks of chaotic oscillators , 2004 .

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

[10]  Luo Runzi,et al.  Combination synchronization of three classic chaotic systems using active backstepping design. , 2011, Chaos.

[11]  Zhenya Yan,et al.  Q-S (lag or anticipated) synchronization backstepping scheme in a class of continuous-time hyperchaotic systems--a symbolic-numeric computation approach. , 2005, Chaos.

[12]  Cun-Fang Feng,et al.  Projective synchronization between two different time-delayed chaotic systems using active control approach , 2010 .

[13]  Xiaofeng Liao,et al.  Complete and lag synchronization of hyperchaotic systems using small impulses , 2004 .

[14]  Jinde Cao,et al.  Adaptive synchronization of uncertain dynamical networks with delayed coupling , 2008 .

[15]  Emad E. Mahmoud,et al.  Complete synchronization of chaotic complex nonlinear systems with uncertain parameters , 2010 .

[16]  Yen-Sheng Chen,et al.  Synchronization of unidirectional coupled chaotic systems via partial stability , 2004 .