| Texto completo | |
| Autor(es): |
Andrade, Kamila da S.
;
Cespedes, Oscar A. R.
;
Cruz, Dayane R.
;
Novaes, Douglas D.
Número total de Autores: 4
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Differential Equations; v. 287, p. 36-pg., 2021-03-29. |
| Resumo | |
In this paper, we are interested in providing lower estimations for the maximum number of limit cycles H(n) that planar piecewise linear differential systems with two zones separated by the curve y = xn can have, where n is a positive integer. For this, we perform a higher order Melnikov analysis for piecewise linear perturbations of the linear center. In particular, we obtain that H (2) >= 4, H (3) >= 8, H(n) >= 7, for n >= 4 even, and H(n) >= 9, for n >= 5 odd. This improves all the previous results for n >= 2. Our analysis is mainly based on some recent results about Chebyshev systems with positive accuracy and Melnikov Theory, which will be developed at any order for a class of nonsmooth differential systems with nonlinear switching manifold. (C) 2021 Elsevier Inc. All rights reserved. (AU) | |
| Processo FAPESP: | 18/16430-8 - Dinâmica global das equações diferenciais não suaves |
| Beneficiário: | Douglas Duarte Novaes |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |
| 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: | 18/13481-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos |
| Beneficiário: | Marco Antônio Teixeira |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |