Singularly perturbed Hopf boundary equilibrium of planar piecewise smooth vector fields

Carvalho, Tiago de; Gonçalves, Luiz Fernando; Freitas, Bruno Rodrigues de

doi:10.1016/j.jde.2025.113454

Singularly perturbed Hopf boundary equilibrium of planar piecewise smooth vector fields

Data

2025

Autores

Carvalho, Tiago de

Gonçalves, Luiz Fernando

Freitas, Bruno Rodrigues de

Resumo

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.

Palavras-chave

Discontinuous differential system, Hopf boundary bifurcation, Singular perturbation

Citação

CARVALHO, Tiago; GONCALVES, Luiz Fernando; FREITAS, Bruno Rodrigues. Singularly perturbed Hopf boundary equilibrium of planar piecewise smooth vector fields. Journal of Differential Equations, Amsterdam, v. 440, pt. 2, e113454, 2025. DOI: 10.1016/j.jde.2025.113454. Disponível em: https://www.sciencedirect.com/science/article/pii/S0022039625004814. Acesso em: 8 dez. 2025.