We studied the existence of homoclinic orbits and the homoclinic bifurcations in planar piecewiselinear 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.
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徐斌,唐云,杨凤红,林木.分段线性连续系统中的同宿分岔[J].动力学与控制学报,2013,11(1):31~35; Xu Bin, Tang Yun, Yang Fenghong, Lin Mu. Homoclinic bifurcations in piecewise-linear systems[J]. Journal of Dynamics and Control,2013,11(1):31-35.