Asymptotic expansion of the heteroclinic bifurcation for the planar normal form of the 1:2 resonance
Roberto, Lucy Any (Universidade Estadual Paulista "Júlio de Mesquita Filho". 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.
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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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