Invariant manifolds and limit periodic sets of discontinuous foliations
Direct Methods for Stability Analysis of Electrical Power Systems
Geometric theory of the singularly perturbed differential equations
| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Estadual Paulista UNESP, Fac Engn Ilha Solteira, Dept Matemat, Rua Rio de Janeiro 266, BR-15385000 Ilha Solteira, SP - Brazil
[2] Univ Estadual Campinas UNICAMP, Inst Matemat Estat & Comp Cient, Dept Matemat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS; v. 16, n. 3, p. 1425-1452, 2017. |
| Web of Science Citations: | 4 |
| Abstract | |
This paper is concerned with a geometric study of singularly perturbed systems of ordinary differential equations expressed by (n - 1)-parameter families of smooth vector fields on RI, where n >= 2. The inherent characteristic of such systems is the presence of an arbitrary number n of time scales. For n - 2, the proposed geometric approach in this paper reports to Fenichel theory of fast-slow systems {[}N. Fenichel, J. Differential Equations, 31 (1979), pp. 53-98]. We extend the three main theorems due to Fenichel {[}N. Fenichel, J. Differential Equations, 31 (1979), pp. 53-98] to systems involving any number of time scales. (AU) | |
| FAPESP's process: | 13/24541-0 - Ergodic and qualitative theory of dynamical systems |
| Grantee: | Claudio Aguinaldo Buzzi |
| Support Opportunities: | Research Projects - Thematic Grants |
| 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 |