Qualitative Analysis of Crossing Limit Cycles in Discontinuous Liénard-Type Differential Systems

Abstract

In this paper, we investigate qualitative properties of crossing limit cycles for a class of discontinuous nonlinear Liénard-type differential systems with two zones separated by a straight line. Firstly, by applying left and right Poincaré mappings we provide two criteria on the existence, uniqueness and stability of a crossing limit cycle. Secondly, by geometric analysis we estimate the position of the unique limit cycle. Several lemmas are given to obtain an explicit upper bound for the amplitude of the limit cycle. Finally, a predator-prey model with nonmonotonic functional response is studied, and Matlab simulations are presented to show the agreement between theoretical results and numerical analysis.