An Example of Piecewise Linear Systems with Infinitely Many Limit Cycles Separated by a Piecewise Linear Curve and Its Perturbations
Year: 2024
Author: Qing Zhang, Zhengdong Du
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 3 : pp. 759–774
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 $ℓ.$
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2024.759
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 3 : pp. 759–774
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Piecewise linear system crossing limit cycle piecewise linear perturbation piecewise smooth switching curve stability.