Stability and perturbations of generalized heteroclinic loops in piecewise smooth systems (Q1617237)

In this paper, the author consider generalized heteroclinic loops in a class of planar piecewise smooth (PWS) systems, which are defined in two domains separated by a switching manifold. A generalized heteroclinic loop has a hyperbolic saddle point in one subsystem and a generalized singular point on the switching manifold. By using the Dulac map in a small neighborhood of the hyperbolic saddle point to estimate the Poincaré map, the author obtains conditions for the stability of a generalized heteroclinic loop. Some sufficient conditions are provided for the cases of at most one and at most two limit cycles existing in a PWS system. An example of a PWS system having exactly two limit cycles is given to show the validity of the analytical result.