Analysis and adaptive synchronization for a new chaotic system

In this paper, a new three-dimensional autonomous chaotic system is presented. There are three control parameters and three different nonlinear terms in the governed equations. The new chaotic system has six equilibrium points. Basic dynamic properties of the new system are investigated via theoretical analysis and numerical simulation. The nonlinear characteristic of the new chaotic system are demonstrated in terms of equilibria, Jacobian matrices, Lyapunov exponents, a dissipative system, Poincaré maps and bifurcations. Then, an adaptive control law is derived to make the states of two identical chaotic systems asymptotically synchronized based on the Lyapunov stability theory. Finally, a numerical simulation is presented to verify the effectiveness of the proposed synchronization scheme.

[1]  Y. J. Cao,et al.  Controlling Chaotic Systems via Phase Space Reconstruction Technique , 2003, Int. J. Bifurc. Chaos.

[2]  Chi-Chuan Hwang,et al.  A linear continuous feedback control of Chua's circuit , 1997 .

[3]  J. Yan,et al.  Adaptive chattering free variable structure control for a class of chaotic systems with unknown bounded uncertainties , 2005 .

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

[5]  Zhi-Hong Guan,et al.  Feedback and adaptive control for the synchronization of Chen system via a single variable , 2003 .

[6]  Ju H. Park.  Adaptive Synchronization of a Unified Chaotic System with an Uncertain Parameter , 2005 .

[7]  Xikui Ma,et al.  Synchronization of chaotic systems with parametric uncertainty using active sliding mode control , 2004 .

[8]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.

[9]  M. Feki.  An adaptive chaos synchronization scheme applied to secure communication , 2003 .

[10]  Chongxin Liu,et al.  A new chaotic attractor , 2004 .

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

[12]  Guanrong Chen,et al.  Analysis of a new chaotic system , 2005 .

[13]  SYNCHRONIZATION OF HIGH-DIMENSIONAL CHAOS GENERATORS BY OBSERVER DESIGN , 1999 .

[14]  Jinhu Lu,et al.  Controlling uncertain Lü system using linear feedback , 2003 .

[15]  Toshimitsu Ushio.  SYNTHESIS OF SYNCHRONIZED CHAOTIC SYSTEMS BASED ON OBSERVERS , 1999 .

[16]  Jinhu Lu,et al.  Adaptive synchronization of uncertain Rossler hyperchaotic system based on parameter identification , 2004 .

[17]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .