Effective construction of Poincaré-Bendixson regions
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Giacomini, Hector (Université de Tours (França). Laboratoire de Mathemátiques et Physique Théorique)
Grau, Maite (Universitat de Lleida. Departament de Matemàtica)

Date:	2017
Abstract:	This paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincaré--Bendixson regions by using transversal curves, that enables us to prove the existence of a limit cycle that has been numerically detected. We apply our results to several known systems, like the Brusselator one or some Liénard systems, to prove the existence of the limit cycles and to locate them very precisely in the phase space. Our method, combined with some other classical tools can be applied to obtain sharp bounds for the bifurcation values of a saddle-node bifurcation of limit cycles, as we do for the Rychkov system.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-1204 Ministerio de Economía y Competitividad MTM2013-40998-P Ministerio de Economía y Competitividad MTM2014-53703-P
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Published in:	Journal of applied analysis and computation, Vol. 7 Núm. 4 (2017) , p. 1549-1569, ISSN 2156-907X

DOI: 10.11948/2017094

Postprint 23 p, 585.1 KB

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