Nonlinear Phenomena in Complex Systems, 2008, Vol.11, No.1, pp.89-93

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2008, Vol.11, No.1, pp.89-93

Shil'nikov Heteroclinic Orbits in a Chaotic System.
Fengyun Sun and Yi Zhao

In this paper, a chaotic system is investigated, which has only three equilibria but exhibits a chaotic attractor for some parameter values. The existence of heteroclinic orbits of Shil'nikov type in the system is proved by using the undetermined coefficient method. As a consequence, the Shil'nikov criterion guarantees that the system has Smale horseshoes. Moreover, the geometric structures of the chaotic attractor can be determined by these heteroclinic orbits.
Key words: chaos, heteroclinic orbits, Shil'nikov criterion

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