Melnikov Method and Detection of Chaos for Non-smooth Systems  

作　　者：Lin-song SHI Yong-kui ZOU Tassilo Küpper 

机构地区：[1]Department of Mathematics,Tsinghua University [2]Departmentt of Mathematics,Jilin University [3]Mathematics Institute,Univeristy of Cologne

出　　处：《Acta Mathematicae Applicatae Sinica》2013年第4期881-896,共16页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.10071030)

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.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.

关 键 词：CHAOS non-smooth dynamical system Melnikov method homoclinic orbit 

分 类 号：O19[理学—数学]