Limit cycle bifurcations in a class of perturbed piecewise smooth systems

摘要

In this paper, we concern with the number of limit cycles in a piecewise polynomial system. First, we give 42 different phase portraits of the unperturbed system with at least one closed orbit. Then, we perturb one phase portrait of them by piecewise polynomials, and consider lower bounds for the maximal numbers of limit cycles emerging from the origin and generalized homoclinic loop, respectively.