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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 (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.
Note: Número d'acord de subvenció MINECO/MTM2016-77278-P
Note: Número d'acord de subvenció MINECO/MTM2013-40998-P
Note: Número d'acord de subvenció AGAUR/2014/SGR-568
Rights: Tots els drets reservats.
Language: Anglès.
Document: article ; recerca ; submittedVersion
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


Preprint
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The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (scientific output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2018-11-12, last modified 2019-02-02



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