Limit cycle bifurcations in a class of piecewise smooth cubic systems with multiple parameters

Abstract

In this paper, we concern with the problem of limit cycle bifurcation for a class of piecewise smooth cubic systems. Using the first order Melnikov function we prove that at least thirteen limit cycles can be bifurcated from periodic solutions surrounding the center.

The number of limit cycles by perturbing a piecewise linear system with three zones

“…The Melnikov function method based on [15] and Lemma 2.1 in [24] plays a key role in studying the maximum number of limit cycles for these systems. There have been many works on the research of limit cycle bifurcation problems of piecewise continuous differential systems, see [16,12,14,4,3,25] and references cited here.…”