Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three Zones

In this paper, we study the number of limit cycles that can bifurcate from a periodic annulus in a discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines. We prove that if the central subsystem, i.e. the system defined between...

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Detalles Bibliográficos
Autores: Pessoa, Claudio [UNESP], Ribeiro, Ronisio [UNESP]
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/241272
Acceso en línea:http://dx.doi.org/10.1142/S0218127422501140
http://hdl.handle.net/11449/241272
Access Level:acceso abierto
Palabra clave:Limit cycles
Melnikov function
Periodic annulus
Piecewise Hamiltonian differential system
Descripción
Sumario:In this paper, we study the number of limit cycles that can bifurcate from a periodic annulus in a discontinuous planar piecewise linear Hamiltonian differential system with three zones separated by two parallel straight lines. We prove that if the central subsystem, i.e. the system defined between the two parallel lines, has a real center and the other subsystems have centers or saddles, then we have at least three limit cycles that appear after perturbations of the periodic annulus. For this, we study the number of zeros of a Melnikov function for piecewise Hamiltonian system and present a normal form for this system in order to simplify the computations.