Research Article
Open Access
Limit Cycles for Continuous Piecewise Linear Systems with Three Zones Having Two Degenerate Subsystems
1
School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
* Corresponding Author:
Kuilin Wu,
[email protected]
Volume 1, Issue 1
2025
Received: 24 August 2025
Accepted: 22 September 2025
Published: 05 November 2025
Article Information
Abstract
This paper deals with continuous piecewise linear differential systems with three zones separated by two parallel straight lines (for short, CPWL3). The number of limit cycles of CPWL3 systems with two degenerate subsystems is not clear. In the paper, we provide a complete study on the maximum number of limit cycles by geometric techniques when the continuous piecewise linear systems with three zones have two degenerate subsystems. During our analysis, we also detect some bifurcation phenomena, such as boundary equilibrium bifurcation, scabbard bifurcation, grazing bifurcation, heteroclinic bifurcation and Hopf bifurcation.
Graphical Abstract
Keywords
limit cycle
piecewise linear systems
bifurcation
Data Availability Statement
Data will be made available on request.
Funding
This work was supported by the Science and Technology Plan Project of Guizhou Province under Grant ZK[2022]G118.
Conflicts of Interest
The authors declare no conflicts of interest.
Ethical Approval and Consent to Participate
Not applicable.
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Cited By (2)
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Ning Xiao, Kuilin Wu. Global phase portraits of Stommel model with boundary equilibria.
Advances in Continuous and Discrete Models, 2026 , 2026 (1).
[CrossRef] -
A. F. Fonseca, J. Llibre, L. F. Mello. Periodic orbits of two particular classes of planar continuous piecewise linear differential systems with three zones separated by two parallel straight lines.
Boletín de la Sociedad Matemática Mexicana, 2026 , 32 (2).
[CrossRef]
* Citation data provided by Crossref Cited-by.
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Xiong, L., & Wu, K. (2025). Limit Cycles for Continuous Piecewise Linear Systems with Three Zones Having Two Degenerate Subsystems. Journal of Mathematics and Interdisciplinary Applications, 1(1), 3–19. https://doi.org/10.62762/JMIA.2025.453419
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TY - JOUR AU - Xiong, Li AU - Wu, Kuilin PY - 2025 DA - 2025/11/05 TI - Limit Cycles for Continuous Piecewise Linear Systems with Three Zones Having Two Degenerate Subsystems JO - Journal of Mathematics and Interdisciplinary Applications T2 - Journal of Mathematics and Interdisciplinary Applications JF - Journal of Mathematics and Interdisciplinary Applications VL - 1 IS - 1 SP - 3 EP - 19 DO - 10.62762/JMIA.2025.453419 UR - https://www.icck.org/article/abs/JMIA.2025.453419 KW - limit cycle KW - piecewise linear systems KW - bifurcation AB - This paper deals with continuous piecewise linear differential systems with three zones separated by two parallel straight lines (for short, CPWL3). The number of limit cycles of CPWL3 systems with two degenerate subsystems is not clear. In the paper, we provide a complete study on the maximum number of limit cycles by geometric techniques when the continuous piecewise linear systems with three zones have two degenerate subsystems. During our analysis, we also detect some bifurcation phenomena, such as boundary equilibrium bifurcation, scabbard bifurcation, grazing bifurcation, heteroclinic bifurcation and Hopf bifurcation. SN - 3070-393X PB - Institute of Central Computation and Knowledge LA - English ER -
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@article{Xiong2025Limit,
author = {Li Xiong and Kuilin Wu},
title = {Limit Cycles for Continuous Piecewise Linear Systems with Three Zones Having Two Degenerate Subsystems},
journal = {Journal of Mathematics and Interdisciplinary Applications},
year = {2025},
volume = {1},
number = {1},
pages = {3-19},
doi = {10.62762/JMIA.2025.453419},
url = {https://www.icck.org/article/abs/JMIA.2025.453419},
abstract = {This paper deals with continuous piecewise linear differential systems with three zones separated by two parallel straight lines (for short, CPWL3). The number of limit cycles of CPWL3 systems with two degenerate subsystems is not clear. In the paper, we provide a complete study on the maximum number of limit cycles by geometric techniques when the continuous piecewise linear systems with three zones have two degenerate subsystems. During our analysis, we also detect some bifurcation phenomena, such as boundary equilibrium bifurcation, scabbard bifurcation, grazing bifurcation, heteroclinic bifurcation and Hopf bifurcation.},
keywords = {limit cycle, piecewise linear systems, bifurcation},
issn = {3070-393X},
publisher = {Institute of Central Computation and Knowledge}
}
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