Periodic orbit bifurcations in planar hysteretic systems without equilibria
This paper is devoted to the analysis of bidimensional piecewise linear systems with hysteresis coming from 3D systems with slow–fast dynamics. We focus our attention on the symmetric case without equilibria, determining the existence of periodic orbits as well as their stability, and possible bifur...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Recursos: | Universidad Pablo de Olavide (UPO) |
| Repositorio: | RIO. Repositorio Institucional Olavide |
| Idioma: | inglés |
| OAI Identifier: | oai:rio.upo.es:10433/22273 |
| Acesso em linha: | https://hdl.handle.net/10433/22273 |
| Access Level: | acceso abierto |
| Palavra-chave: | Bifurcation Hysteresis Periodic Orbit Equilibrium Planar Hysteretic System |
| Resumo: | This paper is devoted to the analysis of bidimensional piecewise linear systems with hysteresis coming from 3D systems with slow–fast dynamics. We focus our attention on the symmetric case without equilibria, determining the existence of periodic orbits as well as their stability, and possible bifurcations. New analytical characterizations of bifurcations in these hysteretic systems are obtained. In particular, bifurcations of periodic orbits from infinity, grazing and saddle-node bifurcations of periodic orbits are studied in detail and the corresponding bifurcation sets are provided. Finally, the study of the hysteretic systems is shown to be useful in detecting periodic orbits for some 3D piecewise linear systems. |
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