Si’lnikov homoclinic orbits in a new chaotic system

Yongxin Jiang and Jianhua Sun

Chaos, Solitons & Fractals, 2007, vol. 32, issue 1, 150-159

Abstract: In the present paper, a new chaotic system is considered, which is a three-dimensional quadratic system and exhibits two 1-scroll chaotic attractors simultaneously with only three equilibria for some parameters. The existence of Si’lnikov homoclinic orbits in this system has been proven by using the undetermined coefficient method. As a result, the Si’lnikov criterion guarantees that the system has Smale horseshoes. Moreover, the geometric structures of attractors are determined by these homoclinic orbits.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:32:y:2007:i:1:p:150-159

DOI: 10.1016/j.chaos.2005.10.088

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