Birth of limit cycles for a classe of continuous and discontinuous differential systems in (d 2)-dimension

The orbits of the reversible differential system ˙x = -y, ˙y = x, ˙z = 0, with x, y ∈ R and z ∈ R d, are periodic with the exception of the equilibrium points (0, 0, z1, . . . , zd). We compute the maximum number of limit cycles which bifurcate from the periodic orbits of the system ˙x = -y, ˙y = x,...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Teixeira, Marco Antonio|||0000-0002-5386-9282, Zeli, Iris O.
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:169449
Acceso en línea:https://ddd.uab.cat/record/169449
https://dx.doi.org/urn:doi:10.1080/14689367.2015.1102868
Access Level:acceso abierto
Palabra clave:Averaging theory
Discontinuous polynomial differential system
Limit cycle
Periodic orbit
Descripción
Sumario:The orbits of the reversible differential system ˙x = -y, ˙y = x, ˙z = 0, with x, y ∈ R and z ∈ R d, are periodic with the exception of the equilibrium points (0, 0, z1, . . . , zd). We compute the maximum number of limit cycles which bifurcate from the periodic orbits of the system ˙x = -y, ˙y = x, ˙z = 0, using the averaging theory of first order, when this system is perturbed, first inside the class of all polynomial differential systems of degree n, and second inside the class of all discontinuous piecewise polynomial differential systems of degree n with two pieces, one in y.