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Volume 6, Issue 3
An Example of Piecewise Linear Systems with Infinitely Many Limit Cycles Separated by a Piecewise Linear Curve and Its Perturbations

Qing Zhang & Zhengdong Du

DOI: 10.12150/jnma.2024.759

J. Nonl. Mod. Anal., 6 (2024), pp. 759-774.

Published online: 2024-08

[An open-access article; the PDF is free to any online user.]

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  • 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 $ℓ.$

  • Keywords

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

  • AMS Subject Headings

34C07, 34C23, 34A36

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-6-759, author = {Zhang , Qing and Du , Zhengdong}, title = {An Example of Piecewise Linear Systems with Infinitely Many Limit Cycles Separated by a Piecewise Linear Curve and Its Perturbations}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2024}, volume = {6}, number = {3}, pages = {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 $ℓ.$

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.759}, url = {http://global-sci.org/intro/article_detail/jnma/23361.html} }
TY - JOUR T1 - An Example of Piecewise Linear Systems with Infinitely Many Limit Cycles Separated by a Piecewise Linear Curve and Its Perturbations AU - Zhang , Qing AU - Du , Zhengdong JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 759 EP - 774 PY - 2024 DA - 2024/08 SN - 6 DO - http://doi.org/10.12150/jnma.2024.759 UR - https://global-sci.org/intro/article_detail/jnma/23361.html KW - Piecewise linear system, crossing limit cycle, piecewise linear perturbation, piecewise smooth switching curve, stability. AB -

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 $ℓ.$

Zhang , Qing and Du , Zhengdong. (2024). 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. 6 (3). 759-774. doi:10.12150/jnma.2024.759
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