On the Hopf-zero bifurcation of the Michelson system
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics)

Date:	2011
Abstract:	Applying a new result for studying the periodic orbits of a differential system via the averaging theory, we provide the first analytic proof on the existence of a Hopf-zero bifurcation for the Michelson system x2 x˙ = y, y˙ = z, z˙ = c2 − y − , 2 at c = 0. Moreover our method estimates the shape of this periodic orbit in function of c > 0 sufficiently small.
Grants:	Ministerio de Ciencia y Tecnología MTM 2005-06098-C02-01 Agència de Gestió d'Ajuts Universitaris i de Recerca 2005/SGR-550
Note:	Agraïments: The second author is partially supported by NNSF of China grant 10671123 and NCET of China grant 050391. He thanks the Centre de Recerca Matemàtica for the hospitality and the financial support by the grant SAB2006-0098 (Ministerio de Educación y Ciencia, Spain).
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Michelson system ; Periodic orbit ; Averaging method
Published in:	Nonlinear Analysis: Real World Applications, Vol. 12 (2011) , p. 1650-1653, ISSN 1468-1218

DOI: 10.1016/j.nonrwa.2010.10.019

Postprint 6 p, 562.3 KB

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