On the periodic orbits of the continuous-discontinuous piecewise differential systems with three pieces separated by two parallel straight lines
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Teixeira, Marco Antonio (Universidade Estadual de Campinas. Departamento de Matemática)

Fecha:	2023
Resumen:	During these last twenty years many papers have been published about the piecewise differential systems in the plane. The increasing interest on these kind of differential systems mainly is due to their big number of applications for modeling many natural phenomena. As usual one of the main difficulties for understanding the dynamics of the differential systems in the plane consists in controlling their periodic orbits and mainly their limit cycles. Therefore there are a big number of papers studying the existence or non-existence of periodic orbits of the continuous and discontinuous piecewise differential systems, but as far as we know this paper will be one of the first papers studying the periodic orbits of a class of piecewise differential systems such that in a part of the line of separation between the two differential systems forming the piecewise differential system is continuous and in the other part it is discontinuous. Thus we shall study the piecewise differential systems separated by two parallel straight lines, in one of these straight lines the piecewise differential system is continuous and in the other discontinuous, moreover in the three pieces of these piecewise differential systems we put arbitrary Hamiltonian systems of degree one. We obtain that such kind of continuous-discontinuous piecewise differential systems cannot have limit cycles, but they can have a continuum of periodic orbits.
Ayudas:	Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
Derechos:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Lengua:	Anglès
Documento:	Article ; recerca ; Versió acceptada per publicar
Materia:	Limit cycles ; Hamiltonian systems ; Continuous piecewise differential systems ; Discontinuous piecewise differential systems
Publicado en:	Communications in nonlinear science and numerical simulation, Vol. 125 (October 2023) , art. 107421, ISSN 1007-5704

DOI: 10.1016/j.cnsns.2023.107421

Disponible a partir de: 2025-10-31 Postprint

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Documentos de investigación > Documentos de los grupos de investigación de la UAB > Centros y grupos de investigación (producción científica) > Ciencias > GSD (Grupo de sistemas dinámicos)
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