Bifurcation Analysis of a Class of Planar Piecewise Smooth Linear-Quadratic System

Abstract

In this paper, we consider a planar piecewise smooth differential system consisting of a linear system and a quadratic Hamiltonian system. The quadratic system has some folds on the discontinuity line. The linear system may have a focus, saddle or node. Our results show that this piecewise smooth differential system will have two limit cycles and a sliding cycle. Moreover, this piecewise smooth system will undergo pseudo-homoclinic bifurcation, Hopf bifurcation and critical crossing bifurcation $CC$. Some examples are given to illustrate our results.