| Texto completo | |
| Autor(es): |
da Silva, Guilherme Tavares
;
Martins, Ricardo Miranda
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | NONLINEAR DYNAMICS; v. 108, n. 4, p. 28-pg., 2022-04-13. |
| Resumo | |
One of the most common hypotheses on the theory of non-smooth dynamical systems is a regular surface as switching manifold, at which case there is at least well-defined and established Filippov dynamics. However, systems with singular switching manifolds still lack such well-established dynamics, although present in many relevant models of phenomena where multiple switches or multiple abrupt changes occur. In this paper, we leverage a methodology that, through blow-ups and singular perturbation, allows to extend Filippov dynamics to the singular case. Specifically, tridimensional systems whose switching manifold consists of an algebraic manifold with transversal self-intersection are considered. This configuration, known as double discontinuity, represents systems with two switches and whose singular part consists of a straight line, where ordinary Filippov dynamics is not directly applicable. For the general, nonlinear case, beyond defining the so-called fundamental dynamics over the singular part, general theorems on its qualitative behavior are provided. For the affine case, however, theorems fully describing the fundamental dynamics are obtained. Finally, this fine-grained control over the dynamics is leveraged to derive Peixoto-like theorems characterizing semi-local structural stability. (AU) | |
| Processo FAPESP: | 18/03338-6 - Dinâmica global de sistemas dinâmicos suaves por partes |
| Beneficiário: | Ricardo Miranda Martins |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| Processo FAPESP: | 21/08031-9 - Campos vetoriais suaves por partes definidos em variedades compactas |
| Beneficiário: | Ricardo Miranda Martins |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| Processo FAPESP: | 18/13481-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos |
| Beneficiário: | Marco Antônio Teixeira |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |