Electron. J. Differential Equations, Vol. 2023 (2023), No. 83, pp. 1-57.

Global analysis on a continuous planar piecewise linear differential system with three zones

Man Jia, Youfeng Su, Hebai Chen

Abstract:
This article concerns the global dynamics of a continuous planar piecewise linear differential system with three zones. We give global phase portraits in the Poincare disc and classify bifurcation diagrams under certain parametric conditions, when the dynamics of central linear zone is anti-saddle. Rich dynamical behaviors are demonstrated, from which we observe homoclinic loops appearing in three linear zones and limit cycles occurring in three linear zones which surround a node or node-focus.

Submitted June 6, 2023. Published December 10, 2023.
Math Subject Classifications: 34C05, 34C23, 37G15, 37G20.
Key Words: Piecewise linear system; global phase portrait; bifurcation; invariant manifold; limit cycle; homoclinic loop.
DOI: 10.58997/ejde.2023.83

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Man Jia
School of Mathematics and Statistics
HNP-LAMA, Central South University
Changsha, Hunan 410083, China
email: jiaman9305@163.com
Youfeng Su
College of Computer and Data Science
Fuzhou University
Fuzhou, Fujian 350116, China
email: yfsu@fzu.edu.cn
Hebai Chen
School of Mathematics and Statistics
HNP-LAMA, Central South University
Changsha, Hunan 410083, China
email: chen_hebai@csu.edu.cn

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