An Example of Piecewise Linear Systems with Infinitely Many Limit Cycles Separated by a Piecewise Linear Curve and Its Perturbations (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we present an example of piecewise linear systemswith infinitely many crossing limit cycles defined in two zones separated bya piecewise linear curve with countable corners. Then we prove that underpiecewise linear perturbations, the perturbed system can have infinitely manylimit cycles, or exactly $ℓ$ limit cycles for any given nonnegative integer $ℓ.$
Keywords: Piecewise linear system; crossing limit cycle; piecewise linear perturbation; piecewise smooth switching curve; stability.