Melnikov Method and Detection of Chaos for Non-smooth Systems

被引：0
|
作者：
Linsong SHI [1 ]
Yongkui ZOU [2 ]
Tassilo Kpper [3 ]
机构：
[1] Department of Mathematics,Tsinghua University
[2] Departmentt of Mathematics,Jilin University
[3] Mathematics Institute,Univeristy of
来源：
Acta Mathematicae Applicatae Sinica(English Series) | 2013年 / 29卷 / 04期
关键词：
D O I：
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中图分类号：
O19 [动力系统理论];
学科分类号：
070104 ; 0711 ; 071101 ;
摘要：
We extend the Melnikov method to non-smooth dynamical systems to study the global behavior near a non-smooth homoclinic orbit under small time-periodic perturbations. The definition and an explicit expression for the extended Melnikov function are given and applied to determine the appearance of transversal homoclinic orbits and chaos. In addition to the standard integral part, the extended Melnikov function contains an extra term which reflects the change of the vector field at the discontinuity. An example is discussed to illustrate the results.
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页码：881 / 896
页数：16
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