| Texto completo | |
| Autor(es): |
Silva, Carlos Vinicius das Neves
;
da Silva, Paulo Ricardo
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | JOURNAL OF NONLINEAR SCIENCE; v. 36, n. 1, p. 42-pg., 2025-10-29. |
| Resumo | |
We study piecewise-smooth systems with three zones, z(center dot)=fi(z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{z} = f_i(z)$$\end{document}, i=1,2,3,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i = 1,2,3,$$\end{document} whose discontinuity set Sigma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Sigma $$\end{document} consists either of a pair of parallel lines or a pair of circles tangent to each other internally or externally. Each fi:C<overline>-> C<overline>\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_i:\overline{\mathbb {C}} \rightarrow \overline{\mathbb {C}}$$\end{document} is assumed to be a holomorphic function. We establish conditions ensuring the existence of limit cycles in such systems and provide lower bounds for the maximum number of limit cycle. Our approach combines the Melnikov method, local integrability properties of holomorphic systems, and the existence of normal forms around zeros and poles. (AU) | |
| Processo FAPESP: | 24/15612-6 - Teorias ergódica e qualitativa dos sistemas dinâmicos III |
| Beneficiário: | Claudio Aguinaldo Buzzi |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 23/02959-5 - Sistemas Não Suaves e Perturbações Singulares |
| Beneficiário: | Paulo Ricardo da Silva |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |