On the Limit Cycles of a Class of Planar Singular Perturbed Differential Equations

Relaxation oscillations of two-dimensional planar singular perturbed systems with a layer equation exhibiting canard cycles are studied. The canard cycles under consideration contain two turning points and two jump points. We suppose that there exist three parameters permitting generic breaking at b...

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Detalles Bibliográficos
Autores principales: Wu, Yuhai, Zhou, Jingjing
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3988861/
https://www.ncbi.nlm.nih.gov/pubmed/25143973
http://dx.doi.org/10.1155/2014/379897
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author Wu, Yuhai
Zhou, Jingjing
author_facet Wu, Yuhai
Zhou, Jingjing
author_sort Wu, Yuhai
collection PubMed
description Relaxation oscillations of two-dimensional planar singular perturbed systems with a layer equation exhibiting canard cycles are studied. The canard cycles under consideration contain two turning points and two jump points. We suppose that there exist three parameters permitting generic breaking at both the turning points and the connecting fast orbit. The conditions of one (resp., two, three) relaxation oscillation near the canard cycles are given by studying a map from the space of phase parameters to the space of breaking parameters.
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spelling pubmed-39888612014-08-20 On the Limit Cycles of a Class of Planar Singular Perturbed Differential Equations Wu, Yuhai Zhou, Jingjing ScientificWorldJournal Research Article Relaxation oscillations of two-dimensional planar singular perturbed systems with a layer equation exhibiting canard cycles are studied. The canard cycles under consideration contain two turning points and two jump points. We suppose that there exist three parameters permitting generic breaking at both the turning points and the connecting fast orbit. The conditions of one (resp., two, three) relaxation oscillation near the canard cycles are given by studying a map from the space of phase parameters to the space of breaking parameters. Hindawi Publishing Corporation 2014-03-31 /pmc/articles/PMC3988861/ /pubmed/25143973 http://dx.doi.org/10.1155/2014/379897 Text en Copyright © 2014 Y. Wu and J. Zhou. https://creativecommons.org/licenses/by/3.0/This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Wu, Yuhai
Zhou, Jingjing
On the Limit Cycles of a Class of Planar Singular Perturbed Differential Equations
title On the Limit Cycles of a Class of Planar Singular Perturbed Differential Equations
title_full On the Limit Cycles of a Class of Planar Singular Perturbed Differential Equations
title_fullStr On the Limit Cycles of a Class of Planar Singular Perturbed Differential Equations
title_full_unstemmed On the Limit Cycles of a Class of Planar Singular Perturbed Differential Equations
title_short On the Limit Cycles of a Class of Planar Singular Perturbed Differential Equations
title_sort on the limit cycles of a class of planar singular perturbed differential equations
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3988861/
https://www.ncbi.nlm.nih.gov/pubmed/25143973
http://dx.doi.org/10.1155/2014/379897
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