Homoclinic and heteroclinic bifurcations in piecewise smooth systems via stability-changing method

In this paper, we study limit cycle bifurcations near homoclinic and heteroclinic loops in piecewise smooth systems with three zones separated by two parallel straight lines. By introducing suitable Poincaré map near a homoclinic loop, we derive some stability criteria and establish bifurcation theory of limit cycles via stability-changing method near homoclinic and heteroclinic loops, respectively. As applications, we give two examples, which consider a class of Liénard piecewise linear differential systems.