Global dynamics of a class of 3-dimensional piecewise linear observable system with two zones

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-04-27 DOI:10.1016/j.physd.2025.134678

Qian Tong, Shimin Li

引用次数: 0

Abstract

Piecewise smooth differential systems have garnered increasing attention due to their broad applications across various fields. Notably, existing literature primarily focuses on planar piecewise smooth systems. In this paper, we investigate a class of 3-dimensional piecewise linear homogeneous observable systems divided into two zones by a plane. We first establish the existence and stability of invariant cones, then analyze the dynamics on these cones utilizing properties of the Poincaré half map. Finally, through Poincaré compactification, we derive the global phase portraits within the Poincaré ball for this 3-dimensional system.

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一类具有两个区域的三维分段线性可观测系统的全局动力学

分段光滑微分系统由于其在各个领域的广泛应用而受到越来越多的关注。值得注意的是，现有文献主要关注平面分段光滑系统。本文研究了一类被平面划分为两个区域的三维分段线性齐次可观测系统。首先建立了不变锥的存在性和稳定性，然后利用庞卡罗半映射的性质分析了不变锥上的动力学。最后，通过poincar紧化，得到了该三维系统在poincarcar球内的全局相图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.