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...

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Detalhes bibliográficos
Autores: Esteban, Marina, Ponce, Enrique, Torres, Francisco
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
Descrição
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.