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

Authors

  • Qing Zhang
  • Zhengdong Du

DOI:

https://doi.org/10.12150/jnma.2024.759

Keywords:

Piecewise linear system, crossing limit cycle, piecewise linear perturbation, piecewise smooth switching curve, stability.

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 $ℓ.$

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Published

2024-08-29

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Issue

Vol. 6 No. 3 (2024)

Section

Articles

How to Cite

An Example of Piecewise Linear Systems with Infinitely Many Limit Cycles Separated by a Piecewise Linear Curve and Its Perturbations. (2024). Journal of Nonlinear Modeling and Analysis, 6(3), 759-774. https://doi.org/10.12150/jnma.2024.759