Limit cycle bifurcations near homoclinic and heteroclinic loops via stability-changing of a homoclinic loop

Abstract

This paper is concerned with the problem of limit cycle bifurcation near a homoclinic or heteroclinic loop for non-smooth systems. By establishing the Poincaré map, some stability criteria are derived for a homoclinic loop in the non-smooth system under study. Furthermore, based on the theory of stability-changing of a homoclinic loop, a new approach is proposed to find limit cycles for the non-smooth system. Finally, several examples are provided to illustrate the obtained results.