Realization of Arbitrary Configuration of Limit Cycles of Piecewise Linear System

TL;DR

This paper demonstrates how any arrangement of Jordan curves can be realized as limit cycles in a plane by a specific type of discontinuous piecewise linear system with two zones separated by a continuous boundary.

Contribution

It introduces a method to realize arbitrary configurations of limit cycles using a simple two-zone piecewise linear system with a continuous separating curve.

Findings

Any configuration of Jordan curves can be realized as limit cycles.

The realization uses a discontinuous piecewise linear system with two zones.

The system is separated by a continuous boundary.

Abstract

In this paper, we consider the realization of configuration of limit cycles of piecewise linear systems on the plane. We show that any configuration of Jordan curves can be realized by a discontinuous piecewise linear system with two zones separated by a continuous curve.