On typical homoclinic-like loops in 3D Filippov systems

Autor(es)

Gomide, Otavio M. L. ^{[1, 2]} ; Teixeira, Marco A. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, IMECC, Dept Math, BR-13083970 Campinas, SP - Brazil

^[2] Univ Fed Goias, IME, Dept Math, BR-74690900 Goiania, Go - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 307, p. 444-475, JAN 15 2022.
• Citações Web of Science: 0

Resumo

In this work a homoclinic-like loop of a 3D piecewise smooth vector field passing through a typical singularity is analyzed. We have shown that such a loop is robust in one-parameter families of Filippov systems. The basin of attraction of this connection is computed as well as its bifurcation diagram. It is worthwhile to mention that this phenomenon has no counterpart in the smooth world. Our approach relies on the analysis of first return maps and the technique used in this scenario is much more complex than the usual analysis of Poincare maps in planar Filippov systems. (C) 2021 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 15/22762-5 - Estabilidade Estrutural de Sistemas Não Suaves em Variedades Tridimensionais
• Beneficiário: Otávio Marçal Leandro Gomide
• Modalidade de apoio: Bolsas no Brasil - Doutorado