| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia - Spain
[2] Univ Estadual Campinas, Dept Matemat, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | NONLINEAR DYNAMICS; v. 82, n. 3, p. 1159-1175, NOV 2015. |
| Web of Science Citations: | 13 |
| Abstract | |
This paper deals with the question of the determinacy of the maximum number of limit cycles of some classes of planar discontinuous piecewise linear differential systems defined in two half-planes separated by a straight line . We restrict ourselves to the non-sliding limit cycles case, i.e., limit cycles that do not contain any sliding segment. Among all cases treated here, it is proved that the maximum number of limit cycles is at most 2 if one of the two linear differential systems of the discontinuous piecewise linear differential system has a focus in , a center, or a weak saddle. We use the theory of Chebyshev systems for establishing sharp upper bounds for the number of limit cycles. Some normal forms are also provided for these systems. (AU) | |
| FAPESP's process: | 12/18780-0 - Geometry of control systems, dynamical and stochastics systems |
| Grantee: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 12/10231-7 - Regularization and minimal sets for non-smooth dynamical systems |
| Grantee: | Douglas Duarte Novaes |
| Support Opportunities: | Scholarships in Brazil - Doctorate |