Integrability and limit cycles of Moon-Rand system

We study the Darboux integrability of the Moon-Rand polynomial differential system. Moreover we study the limit cycles of the perturbed Moon-Rand system bifurcating from the equilibrium point located at the origin, when it is perturbed inside the class of all quadratic polynomial differential system...

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Detalles Bibliográficos
Autores: Barreira, Luis|||0000-0003-4655-5792, Valls, Clàudia|||0000-0001-8279-1229, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:145319
Acceso en línea:https://ddd.uab.cat/record/145319
https://dx.doi.org/urn:doi:10.1016/j.ijnonlinmec.2014.11.029
Access Level:acceso abierto
Palabra clave:Averaging theory
Darboux first integral
Darboux polynomial
Exponential factor
Limit cycles
Descripción
Sumario:We study the Darboux integrability of the Moon-Rand polynomial differential system. Moreover we study the limit cycles of the perturbed Moon-Rand system bifurcating from the equilibrium point located at the origin, when it is perturbed inside the class of all quadratic polynomial differential systems in R3, and we prove that at first order in the perturbation parameter ε the perturbed system can exhibit one limit cycle, and that at second order it can exhibit four limit cycles bifurcating from the origin. We provide explicit expressions of these limit cycles up to order O(ε2).