Home > Articles > Published articles > Asymptotic expansion of the heteroclinic bifurcation for the planar normal form of the 1:2 resonance |
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 |
Postprint 11 p, 287.9 KB |