Singularly perturbed Hopf boundary equilibrium of planar piecewise smooth vector fields

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-05-28 DOI:10.1016/j.jde.2025.113454

Tiago Carvalho , Luiz Fernando Gonçalves , Bruno Rodrigues Freitas

引用次数: 0

Abstract

In this paper, we describe, via singular perturbations and blow-ups, the dynamics around a boundary equilibrium of planar piecewise smooth vector fields. After all desingularizations, we show that the singularly perturbed system has asymptotically attractor equilibria as the ω-limit set.

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平面分段光滑向量场的奇摄动Hopf边界平衡

本文利用奇异摄动和爆破，讨论了平面分段光滑矢量场边界平衡点附近的动力学问题。在所有的去广化之后，我们证明了奇异摄动系统具有渐近吸引平衡点作为ω极限集。

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

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics