Limit cycles of piecewise smooth differential systems of the type nonlinear center and saddle

TL;DR

This paper investigates the maximum number of limit cycles in certain piecewise smooth differential systems with nonlinear centers and Hamiltonian saddles, establishing conditions for their existence and uniqueness.

Contribution

It extends existing results by analyzing systems with nonlinear centers and Hamiltonian saddles separated by parallel lines, identifying the maximum number of limit cycles possible.

Findings

At most one limit cycle exists in these systems.

Systems can have exactly one limit cycle.

Conditions for the existence of the limit cycle are provided.

Abstract

Piecewise linear differential systems separated by two parallel straight lines of the type of center-center-Hamiltonian saddle and the center-Hamiltonian saddle-Hamiltonian saddle can have at most one limit cycle and there are systems in these classes having one limit cycle. In this paper, we study the limit cycles of a piecewise smooth differential system separated by two parallel straight lines formed by nonlinear centers and a Hamiltonian saddle.