Collections of heteroclinic cycles in the Kuramoto-Sivashinsky equation

We study the Kuramoto-Sivashinky equation with periodic boundary conditions in the case of low-dimensional behavior. We analyze the bifurcations that occur in a six-dimensional (6D) approximation of its inertial manifold. We mainly focus on the attracting and structurally stable heteroclinic connect...

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Autores principales: Dawson, S.P., Mancho, A.M.
Formato: JOUR
Materias:
Attracting heteroclinic cycles
Kuramoto-Sivashinsky
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_01672789_v100_n3-4_p231_Dawson
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_01672789_v100_n3-4_p231_Dawson2023-10-03T15:04:33Z Collections of heteroclinic cycles in the Kuramoto-Sivashinsky equation Dawson, S.P. Mancho, A.M. Attracting heteroclinic cycles Kuramoto-Sivashinsky We study the Kuramoto-Sivashinky equation with periodic boundary conditions in the case of low-dimensional behavior. We analyze the bifurcations that occur in a six-dimensional (6D) approximation of its inertial manifold. We mainly focus on the attracting and structurally stable heteroclinic connections that arise for these parameter values. We reanalyze the ones that were previously described via a 4D reduction to the center-unstable manifold (Ambruster et al., 1988, 1989). We also find a parameter region for which a manifold of structurally stable heteroclinic cycles exist. The existence of such a manifold is responsible for an intermittent behavior which has some features of unpredictability. Copyright © 1997 Elsevier Science B.V. All rights reserved. Fil:Dawson, S.P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01672789_v100_n3-4_p231_Dawson
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Attracting heteroclinic cycles
Kuramoto-Sivashinsky
spellingShingle Attracting heteroclinic cycles
Kuramoto-Sivashinsky
Dawson, S.P.
Mancho, A.M.
Collections of heteroclinic cycles in the Kuramoto-Sivashinsky equation
topic_facet Attracting heteroclinic cycles
Kuramoto-Sivashinsky
description We study the Kuramoto-Sivashinky equation with periodic boundary conditions in the case of low-dimensional behavior. We analyze the bifurcations that occur in a six-dimensional (6D) approximation of its inertial manifold. We mainly focus on the attracting and structurally stable heteroclinic connections that arise for these parameter values. We reanalyze the ones that were previously described via a 4D reduction to the center-unstable manifold (Ambruster et al., 1988, 1989). We also find a parameter region for which a manifold of structurally stable heteroclinic cycles exist. The existence of such a manifold is responsible for an intermittent behavior which has some features of unpredictability. Copyright © 1997 Elsevier Science B.V. All rights reserved.
format JOUR
author Dawson, S.P.
Mancho, A.M.
author_facet Dawson, S.P.
Mancho, A.M.
author_sort Dawson, S.P.
title Collections of heteroclinic cycles in the Kuramoto-Sivashinsky equation
title_short Collections of heteroclinic cycles in the Kuramoto-Sivashinsky equation
title_full Collections of heteroclinic cycles in the Kuramoto-Sivashinsky equation
title_fullStr Collections of heteroclinic cycles in the Kuramoto-Sivashinsky equation
title_full_unstemmed Collections of heteroclinic cycles in the Kuramoto-Sivashinsky equation
title_sort collections of heteroclinic cycles in the kuramoto-sivashinsky equation
url http://hdl.handle.net/20.500.12110/paper_01672789_v100_n3-4_p231_Dawson
work_keys_str_mv AT dawsonsp collectionsofheterocliniccyclesinthekuramotosivashinskyequation
AT manchoam collectionsofheterocliniccyclesinthekuramotosivashinskyequation
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