| Full text | |
| Author(s): |
Toniol Cardin, Pedro
[1]
Total Authors: 1
|
| Affiliation: | [1] Univ Estadual Paulista UNESP, Fac Engn, Dept Matemat, BR-15385000 Ilha Solteira, SP - Brazil
Total Affiliations: 1
|
| Document type: | Journal article |
| Source: | Chaos; v. 32, n. 1 JAN 2022. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 19/10269-3 - Ergodic and qualitative theories of dynamical systems II |
| Grantee: | Claudio Aguinaldo Buzzi |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 19/00976-4 - Dynamical systems with multiple time scales |
| Grantee: | Pedro Toniol Cardin |
| Support Opportunities: | Regular Research Grants |