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
Show me the PDF file (4023 KB), TEX file for this article.
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Man Jia School of Mathematics and Statistics HNP-LAMA, Central South University Changsha, Hunan 410083, China email: jiaman9305@163.com |
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Youfeng Su College of Computer and Data Science Fuzhou University Fuzhou, Fujian 350116, China email: yfsu@fzu.edu.cn |
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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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