Stability and Limit Cycle Bifurcation for Two Kinds of Generalized Double Homoclinic Loops in Planar Piecewise Smooth Systems

摘要

In this paper, we present two kinds of generalized double homoclinic loops in planar piecewise smooth systems. For their stability a criterion is provided. Under nondegenerate conditions, we prove that for each case there are at most five limit cycles which can be bifurcated from the generalized double homoclinic loop. Especially, we construct two concrete systems to show that the upper bound can be achieved in both cases.