An Example of Piecewise Linear Systems with Infinitely Many Limit Cycles Separated by a Piecewise Linear Curve and Its Perturbations

Abstract

In this paper, we present an example of piecewise linear systems with infinitely many crossing limit cycles defined in two zones separated by a piecewise linear curve with countable corners. Then we prove that under piecewise linear perturbations, the perturbed system can have infinitely many limit cycles, or exactly $ℓ$ limit cycles for any given nonnegative integer $ℓ.$