Global dynamics of a Filippov system with general parameters and saddle structure of a regular-SN

Abstract

In this paper we investigate the global dynamics of a planar 3-parametric Filippov system with saddle structure of a regular-saddle-node for general parameters. Our work generalizes previous publications in four aspects: vertical switching line to non-vertical, fixed regular direction to non-fixed, small parameters to general, local dynamics to global. Analyzing the qualitative properties of singular points on switching line and in whole Poincaré disc as well as all kinds of closed loops, we obtain the global bifurcation diagram and all corresponding global phase portraits. From our result, in the case of small parameters we find the heteroclinic bifurcation in this system, which does not appear in previous publications. Moreover, in the case of general parameters we find some new bifurcations in this system not appearing for small parameters such as double tangency bifurcation, pseudo-saddle-node bifurcation and some new bifurcation phenomena of boundary node and boundary saddle.