Relaxation oscillation in planar discontinuous piecewise smooth fast-slow systems
| Autor: | Pedro Toniol Cardin |
|---|---|
| Přispěvatelé: | Universidade Estadual Paulista (UNESP) |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Scopus Repositório Institucional da UNESP Universidade Estadual Paulista (UNESP) instacron:UNESP |
| ISSN: | 1089-7682 |
| Popis: | Made available in DSpace on 2022-04-28T19:49:39Z (GMT). No. of bitstreams: 0 Previous issue date: 2022-01-01 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 Γ ϵ when the singular perturbation parameter ϵ is positive and small enough. Moreover, in the singular limit ϵ → 0, the cycle Γ ϵ converges to a crossing closed singular trajectory. We also study the regularization of the crossing relaxation oscillator Γ ϵ 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 ϵ. 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. Departamento de Matemática Faculdade de Engenharia Universidade Estadual Paulista (UNESP) Departamento de Matemática Faculdade de Engenharia Universidade Estadual Paulista (UNESP) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|