| Texto completo | |
| Autor(es): |
Novaes, Douglas Duarte
;
Silva, Leandro A.
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS; v. 24, n. 1, p. 22-pg., 2025-01-01. |
| Resumo | |
The cyclicity problem, crucial in analyzing planar vector fields, consists of estimating the number of limit cycles emanating from monodromic singularities. Traditionally, this estimation relies on Lyapunov coefficients. However, in nonsmooth systems, besides the limit cycles bifurcating by varying the Lyapunov coefficients, monodromic singularities on the switching curve can always be split apart, yielding, under suitable conditions, a sliding region and an additional limit cycle surrounding it. This bifurcation phenomenon, known as pseudo-Hopf bifurcation, has enhanced lower-bound cyclicity estimations for monodromic singularities in Filippov systems. In this study, we push beyond the pseudo-Hopf bifurcation, demonstrating that the destruction of (2k, 2k)-monodromic tangential singularities yields at least k limit cycles surrounding sliding segments. This new bifurcation phenomenon expands our understanding of limit cycle bifurcations in nonsmooth systems and, in addition to the theoretical significance, has practical relevance in various applied models involving switches and abrupt processes. (AU) | |
| Processo FAPESP: | 19/10269-3 - Teorias ergódica e qualitativa dos sistemas dinâmicos II |
| Beneficiário: | Claudio Aguinaldo Buzzi |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 22/09633-5 - Teoria da média no estudo de toros invariantes e comportamento periódico em equações e inclusões diferenciais |
| Beneficiário: | Douglas Duarte Novaes |
| 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 |