A succinct characterization of period annuli in planar piecewise linear differential systems with a straight line of nonsmoothness

TL;DR

This paper provides a complete characterization of when period annuli exist in planar piecewise linear differential systems with a straight line of nonsmoothness, using simple parameter operations.

Contribution

It offers a new, concise criterion for the existence of period annuli in nonsmooth systems based on parameter manipulations.

Findings

Characterization of period annuli existence

Parameter-based criteria for nonsmooth systems

Complete solution to the existence problem

Abstract

We close the problem of the existence of period annuli in planar piecewise linear differential systems with a straight line of nonsmoothness. In fact, a characterization for the existence of such objects is provided by means of a few basic operations on the parameters.