分段线性连续系统中的同宿分岔  

HOMOCLINIC BIFURCATIONS IN PIECEWISE-LINEAR SYSTEMS

作　　者：徐斌[1] 唐云[1] 杨凤红[2] 林木[2] 

机构地区：[1]清华大学数学科学系,北京100084 [2]中央财经大学数学系,北京100084

出　　处：《动力学与控制学报》2013年第1期31-35,共5页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11072274)~~

摘　　要：对于平面上分段线性的连续系统研究了同宿轨的存在性及同宿分岔问题.该系统同宿轨的存在性可以归结为两种情况:一种是由一个可见鞍点和一个可见焦点(或中心)组成的系统;另一种是由两个稳定性相反的结点重合于原点组成的系统.本文对第一种情况给出了同宿轨存在的充要条件,并研究了相应的同宿分岔问题.We studied the existence of homoclinic orbits and the homoclinic bifurcations in planar piecewise linear system. The existence of homoclinic orbit in this system can be divided into two cases, one is a system formed by a visible saddle point and a visible focus （or a center）, the other is a system formed by the coincidence of the original point and two nodes with inverse stability. In this paper, we provided the necessary and sufficient condition for the existence of homoclinic orbit, and then analyzed the homoclinic bifurcation.

关 键 词：分段线性 同宿轨 同宿分岔 

分 类 号：O19[理学—数学]