S˘i’lnikov-type orbits of Lorenz-family systems

Junwei Wang, Meichun Zhao, Yanbin Zhang and Xiaohua Xiong

Physica A: Statistical Mechanics and its Applications, 2007, vol. 375, issue 2, 438-446

Abstract: This paper studies the Lorenz-family system which is known to establish a topological connection among the Lorenz, Chen and Lu¨ systems in the parametric space. The existence of S˘i’lnikov heterclinic orbits is proved using an undetermined coefficient method. As a consequence, the S˘i’lnikov criterion along with some technical conditions guarantees that the Lorenz-family system has both Smale horseshoes and horseshoe type of chaos. It is this heteroclinic orbit that determines the geometric structure of the corresponding chaotic attractor.

Keywords: Lorenz-family system; Heteroclinic orbit; S˘i’lnikov criterion; Undetermined coefficient method (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:375:y:2007:i:2:p:438-446

DOI: 10.1016/j.physa.2006.10.007

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