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

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....

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Bibliographic Details
Published in:Electronic journal of differential equations 2023-12, Vol.2023 (1-??), p.83-57
Main Authors: Jia, Man, Su, Youfeng, Chen, Hebai
Format: Article
Language:English
Subjects:
bifurcation
global phase portrait
homoclinic loop
invariant manifold
limit cycle
piecewise linear system
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Summary: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. For more information see https://ejde.math.txstate.edu/Volumes/2023/83/abstr.html
ISSN:1072-6691
1072-6691
DOI:10.58997/ejde.2023.83