Integrability and limit cycles of Moon-Rand system
Barreira, Luis (Universidade de Lisboa. Departamento de Matemática)
Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemática)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2015
Abstract:	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).
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999
Note:	Agraïments: The first and third authors were supported by Portuguese National Funds through FCT-Fundação para a Ciência e a Tecnologia within the projects PTDC/MAT/117106/2010 and PEst-OE/EEI/LA0009/2013 (CAMGSD). FEDER-UNAB10-4E-378.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Averaging theory ; Darboux first integral ; Darboux polynomial ; Exponential factor ; Limit cycles
Published in:	International Journal of Non-Linear Mechanics, Vol. 69 (2015) , p. 129-136, ISSN 0020-7462

DOI: 10.1016/j.ijnonlinmec.2014.11.029

Postprint 16 p, 637.2 KB

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