| Texto completo | |
| Autor(es): |
Toniol Cardin, Pedro
[1]
Número total de Autores: 1
|
| Afiliação do(s) autor(es): | [1] Univ Estadual Paulista UNESP, Fac Engn, Dept Matemat, BR-15385000 Ilha Solteira, SP - Brazil
Número total de Afiliações: 1
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Chaos; v. 32, n. 1 JAN 2022. |
| Citações Web of Science: | 0 |
| Resumo | |
This paper provides a geometric analysis of relaxation oscillations in the context of planar fast-slow systems with a discontinuous right-hand side. We give conditions that guarantee the existence of a stable crossing limit cycle \& UGamma; epsilon when the singular perturbation parameter epsilon is positive and small enough. Moreover, in the singular limit epsilon \& RARR; 0, the cycle \& UGamma; epsilon converges to a crossing closed singular trajectory. We also study the regularization of the crossing relaxation oscillator \& UGamma; epsilon and show that a (smooth) relaxation oscillation exists for the regularized vector field, which is a smooth fast-slow vector field with singular perturbation parameter epsilon. Our approach uses tools in geometric singular perturbation theory. We demonstrate the results to a number of examples including a model of an arch bridge with nonlinear viscous damping. (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: | 19/00976-4 - Sistemas dinâmicos com múltiplas escalas de tempo |
| Beneficiário: | Pedro Toniol Cardin |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |