一类具有正则鞍结点的平面Filippov系统的全局动力学

Global dynamics of a planar Filippov system with a regular-SN

摘要:

本文研究了一类具有正则鞍结点的平面 Filippov 系统的全局动力学. 该研究针对一般参数，不要求参数充分小. 通过对伪平衡、切点、无穷远平衡点及周期轨的定性分析，本文得到具有8条分岔曲线的全局分岔图，且在庞加莱圆盘上给出了所有的全局相图. 所得结果显示了一些没有出现在充分小参数情形下的新分岔现象.

Abstract:

In this paper, we investigate the global dynamics of a planar Filippov system with a regular-SN for general parameters not required to be sufficiently small. By analyzing the qualitative properties of the pseudo-equilibria, tangent points, equilibria at infinity as well as all kinds of periodic orbits, we obtain the global bifurcation diagram with eight bifurcation curves and give all global phase portraits in Poincare disc. Some new bifurcation phenomena which do not appear in the case of small parameters are finded.