On the limit cycles of the Floquet differential equations
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Rodrigues, Ana (Universidade do Porto(Portugal). Centro de Matemática)

Date:	2014
Abstract:	We provide sufficient conditions for the existence of limit cycles for the Floquet differential equations x˙(t) = Ax(t) + ε(B(t)x(t)+b(t)), where x(t) and b(t) are column vectors of length n, A and B(t) are n×n matrices, the components of b(t) and B(t) are T-periodic functions, the differential equation x˙(t) = Ax(t) has a plane filled with T-periodic orbits, and ε is a small parameter. The proof of this result is based on averaging theory.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	Agraïments: The second author is supported by the Swedish Research Council (VR Grant 2010/5905). The authors would like to thanks the Göran Gustafsson Foundation UU/KTH for financial support.
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Averaging theory ; Floquet differential equation ; Limit cycles ; Periodic solutions
Published in:	Discrete and continuous dynamical systems. Series B, Vol. 19 Núm. 4 (2014) , p. 1129-1136, ISSN 1553-524X

DOI: 10.3934/dcdsb.2014.19.1129

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