带三个区的连续平面片断线性微分系统的全局分析

Pub Date : 2023-12-10 DOI:10.58997/ejde.2023.83
Man Jia, Youfeng Su, Hebai Chen
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引用次数: 0

摘要

本文涉及具有三个区的连续平面片断线性微分系统的全局动力学。我们给出了 Poincare 圆盘中的全局相位图,并对某些参数条件下的分岔图进行了分类,此时中心线性区的动力学是反鞍的。我们展示了丰富的动力学行为,从中观察到在三个线性区中出现的同室循环,以及在围绕节点或节点焦点的三个线性区中出现的极限循环。更多信息请参见 https://ejde.math.txstate.edu/Volumes/2023/83/abstr.html
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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. 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
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