| Author(s): |
Total Authors: 3
|
| Affiliation: | [1] UNESP, Fac Engn Ilha Solteira, Dept Matemat, BR-15385000 Ilha Solteira, SP - Brazil
[2] UNESP, Inst Biociencias Letras & Ciencias Exatas, Dept Matemat, BR-15054000 S J Rio Preto, SP - Brazil
[3] Univ Estadual Campinas, IMECC, BR-13081970 Campinas, SP - Brazil
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | QUARTERLY OF APPLIED MATHEMATICS; v. 72, n. 4, p. 673-687, 2014. |
| Web of Science Citations: | 3 |
| Abstract | |
In this paper we study three time scale singular perturbation problems epsilon x ` = f(x, epsilon, delta), y ` = g(x, epsilon, delta), z ` = delta h(x, delta, delta), where x = (x, y, z) is an element of R-n x R-m x R-p, epsilon and delta are two independent small parameters (0 < epsilon, delta << 1), and f, g, h are C-r functions, where r is big enough for our purposes. We establish conditions for the existence of compact invariant sets (singular points, periodic and homoclinic orbits) when epsilon, delta > 0. Our main strategy is to consider three time scales which generate three different limit problems. In addition, we prove that double regularization of nonsmooth dynamical systems with self-intersecting switching variety provides a class of three time scale singular perturbation problems. (AU) | |
| FAPESP's process: | 13/21947-6 - Geometric theory of the singularly perturbed differential equations |
| Grantee: | Pedro Toniol Cardin |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 12/18780-0 - Geometry of control systems, dynamical and stochastics systems |
| Grantee: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |