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.%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.
展开▼
