Existence and Uniqueness of Limit Cycle in Discontinuous Planar Differential Systems

Abstract

In this paper, we investigate the existence and uniqueness of limit cycle for a class of discontinuous planar piecewise smooth differential systems with four regions separated by three vertical parallel lines. We first show the continuity and qualitative properties of half Poincare mappings, and then by some analysis techniques we provide several criteria concerning the existence, uniqueness and stability of limit cycle for the discontinuous planar differential system. Finally, an example possessing a unique stable sliding limit cycle is presented to illustrate the obtained result.