Decomposition Method for Studying Smooth Chua's equation with Application to hyperchaotic multiscroll attractors

This paper focuses on the numerical study of chaotic dynamics via the Adomian decomposition method. The approach, which provides series solutions of the system equations, is first applied to Chua's circuit and Chua's oscillator, both with cubic nonlinearity. Successively, the method is utilized for obtaining hyperchaotic multiscroll attractors in a ring of three Chua's circuits, where the smooth nonlinearities are Hermite interpolating polynomials. The reported examples show that the approach presents two main features, i.e. the system nonlinearity is preserved and the chaotic solution is provided in a closed form.

[1]  C. Wu,et al.  Chua's Equation with Cubic Nonlinearity , 1996 .

[2]  Giuseppe Grassi,et al.  Hyperchaotic Coupled Chua Circuits: an Approach for Generating New n×m-scroll attractors , 2003, Int. J. Bifurc. Chaos.

[3]  Leon O. Chua,et al.  Chua's circuit 10 years later , 1994, Int. J. Circuit Theory Appl..

[4]  Akio Tsuneda,et al.  A Gallery of attractors from Smooth Chua's equation , 2005, Int. J. Bifurc. Chaos.

[5]  Giuseppe Grassi,et al.  Experimental realization of observer-based hyperchaos synchronization , 2001 .

[6]  C. F. Lorenzo,et al.  Chaos in a fractional order Chua's system , 1995 .

[7]  Wenhai Chen,et al.  An algorithm for Adomian decomposition method , 2004, Appl. Math. Comput..

[8]  G. Zhong.  Implementation of Chua's circuit with a cubic nonlinearity , 1994 .

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

[10]  Rabinder N Madan,et al.  Chua's Circuit: A Paradigm for Chaos , 1993, Chua's Circuit.

[11]  Giuseppe Grassi,et al.  A New Phenomenon in nonautonomous Chua's Circuits: Generation of Chaotic Beats , 2004, Int. J. Bifurc. Chaos.

[12]  Giuseppe Grassi,et al.  Chaotic Beats in a Modified Chua's Circuit: Dynamic Behavior and Circuit Design , 2004, Int. J. Bifurc. Chaos.

[13]  Michael Peter Kennedy,et al.  A Fast and Simple Implementation of Chua's oscillator with cubic-like Nonlinearity , 2005, Int. J. Bifurc. Chaos.

[14]  S. Mascolo,et al.  CONTROLLING CHAOTIC DYNAMICS USING BACKSTEPPING DESIGN WITH APPLICATION TO THE LORENZ SYSTEM AND CHUA'S CIRCUIT , 1999 .

[15]  G. Adomian.  A review of the decomposition method and some recent results for nonlinear equations , 1990 .

[16]  Jianhong Wu,et al.  Numerical steady state and Hopf bifurcation analysis on the diffusive Nicholson's blowflies equation , 2000, Appl. Math. Comput..

[17]  George Adomian,et al.  Modified Adomian Polynomials , 1996 .

[18]  Giuseppe Grassi,et al.  On the Generation of Chaotic Beats in Simple nonautonomous Circuits , 2005, Int. J. Bifurc. Chaos.

[19]  Giuseppe Grassi,et al.  New 3D-scroll attractors in hyperchaotic Chua's Circuits Forming a Ring , 2003, Int. J. Bifurc. Chaos.