Impulsive homoclinic chaos in Van der Pol Jerk system

被引：0
|
作者：
Ding Y. [1 ,2 ]
Zhang Q. [1 ]
机构：
[1] School of Mechanical Engineering, Tianjin University
[2] School of Sciences, Tianjin University of Science and Technology
来源：
Transactions of Tianjin University | 2010年 / 16卷 / 06期
基金：
中国国家自然科学基金;
关键词：
chaotic system; homoclinic orbit; Silnikov theorem;
D O I：
10.1007/s12209-010-1400-8
中图分类号：
学科分类号：
摘要：
A 3D continuous autonomous chaotic system is reported, which contains a cubic term and six system parameters. Basic dynamic properties of the new Van der Pol Jerk system are studied by means of theoretical analysis and numerical simulation. Based on the Silnikov theorem, the chaotic characterisitics of the dynamic system are discussed. Using Cardano formula and series solution of differential equation, eigenvalue problem and the existence of homoclinic orbit are studied. Furthermore, a rigorous proof for the existence of Silnikov-sense Smale horseshoes chaos is presented and some conditions which lead to the chaos are obtained. The formation mechanism indicates that this chaotic system has impulsive homoclinic chaos, and numerical simulation demonstrates that there is a route to chaos. © 2010 Tianjin University and Springer-Verlag Berlin Heidelberg.
引用
收藏
页码：457 / 460
页数：3
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