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

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• 作者：Junwei Wang ; Meichun Zhao ; Yanbin Zhang ; Xiaohua Xiong
• 关键词：Lorenz-family system ; Heteroclinic orbit ; S˘ ; i’ ; lnikov criterion ; Undetermined coefficient method
• 刊名：Physica A
• 出版年：2007
• 出版时间：1 March 2007
• 年：2007
• 卷：375
• 期：2
• 页码：438-446
• 全文大小：259 K

文摘

This paper studies the Lorenz-family system which is known to establish a topological connection among the Lorenz, Chen and L 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.