| Texto completo | |
| Autor(es): |
Messias, Marcelo
;
Candido, Murilo R.
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | CHAOS SOLITONS & FRACTALS; v. 182, p. 12-pg., 2024-04-11. |
| Resumo | |
In this paper we consider a simple dissipative oscillator, determined by a two-parameter three-dimensional system of ordinary differential equations, obtained from the Nos & eacute;-Hoover oscillator by adding a small antidamping term in its third equation. Based on numerical evidence, complex dynamics of this system was presented in a recent paper, such as the coexistence of periodic orbits, chaotic attractors and a stable invariant torus. Here we analytically prove the existence of a small periodic orbit from which a stable invariant torus bifurcates near the origin of the dissipative oscillator. We also show that the oscillations near the torus present a kind of relaxation oscillation behavior, like canard-type oscillations, commonly found in singularly perturbed systems. The obtained results extend and provide analytical proofs for some dynamical properties of the considered system, which were numerically described in the literature. (AU) | |
| Processo FAPESP: | 23/06076-0 - Métodos baseados em teoria averaging para detecção de variedades invariantes compactas |
| Beneficiário: | Murilo Rodolfo Cândido |
| Modalidade de apoio: | Auxílio à Pesquisa - Jovens Pesquisadores |
| Processo FAPESP: | 19/10269-3 - Teorias ergódica e qualitativa dos sistemas dinâmicos II |
| Beneficiário: | Claudio Aguinaldo Buzzi |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |