Asymptotic expansion of the heteroclinic bifurcation for the planar normal form of the 1:2 resonance
Roberto, Lucy Any (UNESP (Brasil). Departamento de Matemática)
Da Silva, Paulo R. (UNESP (Brazil). Departamento de Matemática)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2016
Abstract:	We consider the family of planar differential systems depending on two real parameters \[ x =y, y = _1 x _2 y x^3-x^2y. \] This system corresponds to the normal form for the 1:2 resonance which exhibits a heteroclinic connection. The phase portrait of the system has a limit cycle which disappears in the heteroclinic connection for the parameter values on the curve _2=c(_1)=-15_1 O(_1^2), _1<0. We significantly improve the knowledge of this curve in a neighborhood of the origin.
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 318999
Note:	Agraïments: The first author is partially supported by CAPES and FAPESP. The second author is partially supported by CAPES, CNPq-Brazil, and FAPESP.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	1:2 Resonance ; Bifurcation diagram ; Homoclinic Connections ; Planar Systems
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 26 Núm. 1 (2016) , p. 1650017 (8 pages), ISSN 1793-6551

DOI: 10.1142/S0218127416500176

Postprint 11 p, 287.9 KB

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