Constructing a chaotic system with any number of equilibria

被引：229

作者：

Wang, Xiong ^{[1
]}

Chen, Guanrong ^{[1
]}

机构：

[1] City Univ Hong Kong, Dept Elect Engn, Hong Kong, Hong Kong, Peoples R China

来源：

NONLINEAR DYNAMICS | 2013年 / 71卷 / 03期

关键词：

Chaotic system; Equilibrium; Chaotic attractor; Stable chaos; BIFURCATION;

D O I：

10.1007/s11071-012-0669-7

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

In the chaotic Lorenz system, Chen system and Rossler system, their equilibria are unstable and the number of the equilibria are no more than three. This paper shows how to construct some simple chaotic systems that can have any preassigned number of equilibria. First, a chaotic system with no equilibrium is presented and discussed. Then a methodology is presented by adding symmetry to a new chaotic system with only one stable equilibrium, to show that chaotic systems with any preassigned number of equilibria can be generated. By adjusting the only parameter in these systems, one can further control the stability of their equilibria. This result reveals an intrinsic relationship of the global dynamical behaviors with the number and stability of the equilibria of a chaotic system.

引用

页码：429 / 436

页数：8

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