Constructing a chaotic system with any number of equilibria

Xiong Wang; Guanrong Chen

doi:10.1007/s11071-012-0669-7

Constructing a chaotic system with any number of equilibria

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Overview

251 Scopus Citations

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Author(s)

Xiong Wang
Guanrong Chen

Related Research Unit(s)

Department of Electrical Engineering

Detail(s)

Original language	English
Pages (from-to)	429-436
Journal / Publication	Nonlinear Dynamics
Volume	71
Issue number	3
Online published	8 Nov 2012
Publication status	Published - Feb 2013

Link(s)

DOI	DOI https://doi.org/10.1007/s11071-012-0669-7 Final Published version
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Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-84878695597&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(c337e1e8-1a41-4812-b26a-f599afb5b0b3).html

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.