When Parallels and Meridians are Limit Cycles for Polynomial Vector Fields on Quadrics of Revolution in the Euclidean 3-Space-Reference-Cited by-同舟云学术

When Parallels and Meridians are Limit Cycles for Polynomial Vector Fields on Quadrics of Revolution in the Euclidean 3-Space

Published:2016-08 Issue:09 Volume:26 Page:1650160
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Dias Fabio Scalco¹,Llibre Jaume²,Mello Luis Fernando¹

Affiliation:

1. Instituto de Matemática e Computação, Universidade Federal de Itajubá, Avenida BPS 1303, Pinheirinho, CEP 37.500-903, Itajubá, MG, Brazil

2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

Abstract

We study polynomial vector fields of arbitrary degree in [Formula: see text] with an invariant quadric of revolution. We characterize all the possible configurations of invariant meridians and parallels that these vector fields can exhibit. Furthermore, we analyze when these invariant meridians and parallels can be limit cycles.

Funder

Fundação de Amparo à Pesquisa do Estado de Minas Gerais

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Ministerio de Economía y Competitividad

Departament d'Innovació, Universitats i Empresa, Generalitat de Catalunya

European Community Project

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

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