The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems

We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ(3).

Detalles Bibliográficos
Autores principales: Jiang, Yanan, Han, Maoan, Xiao, Dongmei
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/PMC3984815/
https://www.ncbi.nlm.nih.gov/pubmed/24982980
http://dx.doi.org/10.1155/2014/705703
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author Jiang, Yanan
Han, Maoan
Xiao, Dongmei
author_facet Jiang, Yanan
Han, Maoan
Xiao, Dongmei
author_sort Jiang, Yanan
collection PubMed
description We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ(3).
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spelling pubmed-39848152014-06-30 The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems Jiang, Yanan Han, Maoan Xiao, Dongmei ScientificWorldJournal Research Article We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ(3). Hindawi Publishing Corporation 2014 2014-03-26 /pmc/articles/PMC3984815/ /pubmed/24982980 http://dx.doi.org/10.1155/2014/705703 Text en Copyright © 2014 Yanan Jiang et al. 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
Jiang, Yanan
Han, Maoan
Xiao, Dongmei
The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems
title The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems
title_full The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems
title_fullStr The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems
title_full_unstemmed The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems
title_short The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems
title_sort existence of periodic orbits and invariant tori for some 3-dimensional quadratic systems
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3984815/
https://www.ncbi.nlm.nih.gov/pubmed/24982980
http://dx.doi.org/10.1155/2014/705703
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