Existence of Four-Intersection-Point Limit Cycles with Only Saddles Separated by Two Parallel Straight Lines in Planar Piecewise Linear Systems

Abstract

In this paper, we study a family of planar piecewise linear systems with saddles separated by two parallel lines, and mainly investigate the existence of four-intersection-point limit cycles. We provide complete conclusions on the existence of a special four-intersection-point limit cycle and a heteroclinic loop. And, based on these results, we give some sufficient conditions for the existence of general four-intersection-point limit cycles. Some examples are given to illustrate the main results.