Qualitative Analysis of Crossing Limit Cycles in Discontinuous Liénard-Type Differential Systems (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we investigate qualitative properties of crossing limitcycles for a class of discontinuous nonlinear Liénard-type differential systemswith two zones separated by a straight line. Firstly, by applying left and rightPoincaré mappings we provide two criteria on the existence, uniqueness andstability of a crossing limit cycle. Secondly, by geometric analysis we estimatethe position of the unique limit cycle. Several lemmas are given to obtain anexplicit upper bound for the amplitude of the limit cycle. Finally, a predator-prey model with nonmonotonic functional response is studied, and Matlabsimulations are presented to show the agreement between theoretical resultsand numerical analysis.
Keywords: Discontinuous Liénard-type differential system; crossing limit cycle; existence; uniqueness; stability; position.