Constructing a chaotic system with any number of equilibria

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

245 Scopus Citations
View graph of relations

Author(s)

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)429-436
Journal / PublicationNonlinear Dynamics
Volume71
Issue number3
Online published8 Nov 2012
Publication statusPublished - Feb 2013

Abstract

In the chaotic Lorenz system, Chen system and Rössler 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.

Research Area(s)

  • Chaotic attractor, Chaotic system, Equilibrium, Stable chaos

Citation Format(s)

Constructing a chaotic system with any number of equilibria. / Wang, Xiong; Chen, Guanrong.
In: Nonlinear Dynamics, Vol. 71, No. 3, 02.2013, p. 429-436.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review