Limit cycles bifurcating from a zero-Hopf singularity in arbitrary dimension
Barreira, Luis (Instituto Superior Técnico (Portugal). Departamento de Matemática)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemàtica)

Date:	2018
Abstract:	We study the limit cycles which can bifurcate from a zero--Hopf singularity of a C^m 1 differential system in \R^n, i. e. from a singularity with eigenvalues b i and n-2 zeros for n 3. If this singularity is at the origin of coordinates and the Taylor expansion of the differential system at the origin without taking into account the linear terms starts with terms of order m, from the origin it can bifurcate s limit cycles with s \ 0,1, 2^n-3\ if m=2 (see LZ), with s \ 0,1, 3^n-2\ if m=3, with s 6^n-2 if m=4, and with s 4 5^n-2 if m=5. Moreover, s \0,1,2\ if m=4 and n=3, and s \0,1,2,3,4,5\ if m=5 and n=3. Note that the maximum number of limit cycles bifurcating from this zero--Hopf singularity grows up exponentially with the dimension for m=2,3.
Grants:	Ministerio de Economía y Competitividad MTM2016-77278-P Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycles ; Zero-Hopf singularity ; Arbitrary dimension
Published in:	Nonlinear dynamics, Vol. 92, issue 3 (May 2018) , p. 1159-1166, ISSN 0924-090X

DOI: 10.1007/s11071-018-4115-3

Postprint 13 p, 712.8 KB

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