Generating one-, two-, three- and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system

A new four-dimensional quadratic smooth autonomous chaotic system is presented in this paper, which can exhibit periodic orbit and chaos under the conditions on the system parameters. Importantly, the system can generate one-, two-, three- and four-scroll chaotic attractors with appropriate choices of parameters. Interestingly, all the attractors are generated only by changing a single parameter. The dynamic analysis approach in the paper involves time series, phase portraits, Poincare maps, a bifurcation diagram, and Lyapunov exponents, to investigate some basic dynamical behaviours of the proposed four-dimensional system.

[1]  Alberto Tesi,et al.  Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems , 1992, Autom..

[2]  Andrey Shilnikov,et al.  On bifurcations of the Lorenz attractor in the Shimizu-Morioka model , 1993 .

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

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

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

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

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

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

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

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

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

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

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

[14]  Guanrong Chen,et al.  On a four-dimensional chaotic system , 2005 .

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

[16]  L Wang.  Yet another 3D quadratic autonomous system generating three-wing and four-wing chaotic attractors. , 2009, Chaos.

[17]  Daizhan Cheng,et al.  A New Chaotic System and Beyond: the Generalized Lorenz-like System , 2004, Int. J. Bifurc. Chaos.

[18]  Guanrong Chen,et al.  A New Chaotic System and its Generation , 2003, Int. J. Bifurc. Chaos.

[19]  J. Sprott,et al.  Some simple chaotic flows. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[21]  Leon O. Chua,et al.  Simplest chaotic nonautonomous circuit , 1984 .

[22]  Barend Jacobus van Wyk,et al.  A four-wing attractor and its analysis , 2009 .

[23]  Guanrong Chen,et al.  Analysis and circuit implementation of a new 4D chaotic system , 2006 .

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