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A CHAOTIC SYSTEM WITH ONE SADDLE AND TWO STABLE NODE-FOCI

QIGUI YANG

School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, P. R. China

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and

GUANRONG CHEN

Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, P. R. China

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https://doi.org/10.1142/S0218127408021063Cited by:169 (Source: Crossref)

Abstract

This paper reports the finding of a chaotic system with one saddle and two stable node-foci in a simple three-dimensional (3D) autonomous system. The system connects the original Lorenz system and the original Chen system and represents a transition from one to the other. The algebraical form of the chaotic attractor is very similar to the Lorenz-type systems but they are different and, in fact, nonequivalent in topological structures. Of particular interest is the fact that the chaotic system has a chaotic attractor, one saddle and two stable node-foci. To further understand the complex dynamics of the system, some basic properties such as Lyapunov exponents, bifurcations, routes to chaos, periodic windows, possible chaotic and periodic-window parameter regions, and the compound structure of the system are analyzed and demonstrated with careful numerical simulations.

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