Generating variable number of wings from a novel four-dimensional hyperchaotic system with one equilibrium

Abstract In this paper, a novel four-dimensional smooth system is presented. What particularly interests us is that the novel multi-wing chaotic system has only one equilibrium point at the origin. Furthermore, the strange phenomenon that different chaotic attractors such as the two-wing, three-wing chaotic attractors and four-wing hyperchaotic attractor could be generated by changing a single system parameter makes this system unique. By applying either analytical or numerical methods, basic properties of the system such as phase portraits, Poincare mapping, bifurcation diagram and Lyapunov exponents are investigated to observe chaotic motions. The physical existences of the multi-wing chaotic attractors are verified by an electronic circuit.

[1]  Ahmed S. Elwakil,et al.  Creation of a complex butterfly attractor using a novel Lorenz-Type system , 2002 .

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

[3]  Zhuzhi Yuan,et al.  A single three-wing or four-wing chaotic attractor generated from a three-dimensional smooth quadratic autonomous system , 2008 .

[4]  Weihua Deng,et al.  Generating multi-directional multi-scroll chaotic attractors via a fractional differential hysteresis system , 2007 .

[5]  Guanrong Chen,et al.  A four-wing chaotic attractor generated from a new 3-D quadratic autonomous system , 2008 .

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

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

[8]  Ahmed S. Elwakil,et al.  Experimental Verification of the Butterfly Attractor in a Modified Lorenz System , 2002, Int. J. Bifurc. Chaos.

[9]  P. Jarry,et al.  “LORENZ ATTRACTOR” FROM DIFFERENTIAL EQUATIONS WITH PIECEWISE-LINEAR TERMS , 1993 .

[10]  Xinghuo Yu,et al.  Design and Implementation of Grid Multiwing Butterfly Chaotic Attractors From a Piecewise Lorenz System , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[11]  Xinghuo Yu,et al.  Chaos control : theory and applications , 2003 .

[12]  O. Rössler.  An equation for continuous chaos , 1976 .

[13]  Frank C. Hoppensteadt,et al.  Analysis and simulation of chaotic systems , 1992 .

[14]  L. Chua,et al.  The double scroll family , 1986 .

[15]  Sara Dadras,et al.  A novel three-dimensional autonomous chaotic system generating two, three and four-scroll attractors , 2009 .

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