论文信息 - A computer-assisted proof for the existence of horseshoe in a novel chaotic system

A computer-assisted proof for the existence of horseshoe in a novel chaotic system

Abstract The dynamics of a novel chaotic system are studied, and a rigorous computer-assisted proof for existence of horseshoe in this system is given. A Poincare section is properly chosen to obtain the Poincare map, which is proved to be semi-conjugate to the 4-shift map by utilizing topological horseshoe theory. This implies the entropy of the system is no less than log 4, and the system definitely exhibits chaos.

[1] Qingdu Li,et al. Horseshoe in a two-scroll control system , 2004 .

[2] Zengqiang Chen,et al. A novel hyperchaos system only with one equilibrium , 2007 .

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

[4] Daizhan Cheng,et al. Bridge the Gap between the Lorenz System and the Chen System , 2002, Int. J. Bifurc. Chaos.

[5] Xiao-Song Yang,et al. Existence of Horseshoe in a Foodweb Model , 2004, Int. J. Bifurc. Chaos.

[6] Xiao-Song Yang,et al. Horseshoes in piecewise continuous maps , 2004 .

[7] 熊金城. A NOTE ON TOPOLOGICAL ENTROPY , 1989 .

[8] Xiao-Song Yang,et al. Horseshoes in modified Chen’s attractors , 2005 .

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

[10] C. Sparrow. The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors , 1982 .

[11] Xiao-Song Yang,et al. Horseshoe Chaos in Cellular Neural Networks , 2006, Int. J. Bifurc. Chaos.

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

[13] Zhuzhi Yuan,et al. The evolution of a novel four-dimensional autonomous system: Among 3-torus, limit cycle, 2-torus, chaos and hyperchaos , 2009 .

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

[15] Xiao-Song Yang,et al. A new proof for existence of horseshoe in the Rössler system , 2003 .