A novel three-dimensional autonomous chaotic system generating two, three and four-scroll attractors

In this Letter a novel three-dimensional autonomous chaotic system is proposed. Of particular interest is that this novel system can generate two, three and four-scroll chaotic attractors with variation of a single parameter. By applying either analytical or numerical methods, basic properties of the system, such as dynamical behaviors (time history and phase diagrams), Poincare mapping, bifurcation diagram and Lyapunov exponents are investigated to observe chaotic motions. The obtained results clearly show that this is a new chaotic system which deserves further detailed investigation.

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

[2]  Yurong Liu,et al.  Global asymptotic stability of generalized bi-directional associative memory networks with discrete and distributed delays , 2006 .

[3]  Liu Chong-Xin,et al.  A new butterfly-shaped attractor of Lorenz-like system , 2006 .

[4]  Chongxin Liu.  A novel chaotic attractor , 2009 .

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

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

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

[8]  Dequan Li,et al.  A three-scroll chaotic attractor , 2008 .

[9]  Robert C. Hilborn,et al.  Chaos And Nonlinear Dynamics: An Introduction for Scientists and Engineers , 1994 .

[10]  S. Wiggins.  Introduction to Applied Nonlinear Dynamical Systems and Chaos , 1989 .

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

[12]  Wenbo Liu,et al.  2 × 2-scroll attractors Generated in a Three-Dimensional Smooth Autonomous System , 2007, Int. J. Bifurc. Chaos.

[13]  O. Rössler.  CONTINUOUS CHAOS—FOUR PROTOTYPE EQUATIONS , 1979 .

[14]  Tao Liu,et al.  A novel three-dimensional autonomous chaos system , 2009 .

[15]  Guanrong Chen,et al.  The compound structure of a new chaotic attractor , 2002 .

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

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

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

[19]  Lin Wang,et al.  3-scroll and 4-scroll chaotic attractors generated from a new 3-D quadratic autonomous system , 2009 .