| Texto completo | |
| Autor(es): |
De Maesschalck, Peter
;
Huzak, Renato
;
Perez, Otavio Henrique
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Differential Equations; v. 460, p. 32-pg., 2026-01-05. |
| Resumo | |
The main purpose of this paper is to study limit cycles of non-linear regularizations of planar piecewise smooth systems. We deal with a slow-fast Hopf point after non-linear regularization and blow-up. We simple criterion for the existence of limit cycles of canard type blue for a class of (non-linearly) regularized piecewise smooth systems, expressed in terms of zeros of the slow divergence integral. Using the criterion we can construct a quadratic regularization of a piecewise linear center such that for any integer k has at least k + 1 limit cycles, for a suitably chosen monotonic transition function phi k : R -> R. We a similar result for regularized codimension 1 invisible-invisible fold-fold singularities of type II2. cycles of dodging layer are also considered, and we prove that there can be at most 2 limit cycles (born saddle-node bifurcation). (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, similar technologies. (AU) | |
| Processo FAPESP: | 21/10198-9 - Variedades invariantes e conjuntos periódicos limite de folheações descontínuas |
| Beneficiário: | Otavio Henrique Perez |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |
| Processo FAPESP: | 24/00392-0 - Ciclos deslizantes de regularizações de campos de vetores suaves por partes tendo tangencias de ordem alta |
| Beneficiário: | Otavio Henrique Perez |
| Modalidade de apoio: | Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado |