On structural stability of 3D Filippov systems: A semi-local approach

Autor(es)

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

Afiliação do(s) autor(es)

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

• Tipo de documento: Artigo Científico
• Fonte: MATHEMATISCHE ZEITSCHRIFT; v. 294, n. 1-2, p. 419-449, FEB 2020.
• Citações Web of Science: 0

Resumo

The main purpose of this work is to provide a non-local approach to study aspects of structural stability of 3D Filippov systems. We introduce a notion of semi-local structural stability which detects when a piecewise smooth vector field is robust around the entire switching manifold, as well as, provides a complete characterization of such systems. In particular, we present some methods in the qualitative theory of piecewise smooth vector fields, which make use of geometrical analysis of the foliations generated by their orbits. Such approach displays surprisingly rich dynamical behavior which is studied in detail in this work. It is worth mentioning that this subject has not been treated in dimensions higher than two from a non-local point of view, and we hope that the approach adopted herein contributes to the understanding of structural stability for piecewise-smooth vector fields in its most global sense. (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
• Processo FAPESP: 12/18780-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Marco Antônio Teixeira
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 16/23716-0 - Fenômenos globais em sistemas dinâmicos suaves por partes
• Beneficiário: Otávio Marçal Leandro Gomide
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Doutorado