Designable Dynamical Systems for the Generalized Landau Scenario and the Nonlinear Complexification of Periodic Orbits

We have found a way for penetrating the space of the dynamical systems towards systems of arbitrary dimension exhibiting the nonlinear mixing of a large number of oscillation modes through which extraordinarily complex time evolutions arise. The system design is based on assuring the occurrence of a...

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Detalles Bibliográficos
Autores: Herrero Simon, Ramon|||0000-0001-5572-1540, Farjas Silva, Jordi, Pi Vila, Francesc, Orriols Tubella, Gaspar
Tipo de recurso: informe técnico
Fecha de publicación:2021
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/345842
Acceso en línea:https://hdl.handle.net/2117/345842
Access Level:acceso abierto
Palabra clave:Bifurcation theory
Dynamics
Bifurcació, Teoria de la
Dinàmica
Àrees temàtiques de la UPC::Física
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spelling Designable Dynamical Systems for the Generalized Landau Scenario and the Nonlinear Complexification of Periodic OrbitsHerrero Simon, Ramon|||0000-0001-5572-1540Farjas Silva, JordiPi Vila, FrancescOrriols Tubella, GasparBifurcation theoryDynamicsBifurcació, Teoria de laDinàmicaÀrees temàtiques de la UPC::FísicaWe have found a way for penetrating the space of the dynamical systems towards systems of arbitrary dimension exhibiting the nonlinear mixing of a large number of oscillation modes through which extraordinarily complex time evolutions arise. The system design is based on assuring the occurrence of a number of Hopf bifurcations in a set of fixed points of a relatively generic system of ordinary differential equations, in which the main peculiarity is that the nonlinearities appear through functions of a linear combination of the system variables. The paper presents the design procedure and a selection of numerical simulations with a variety of designed systems whose dynamical behaviors are really rich and full of unknown features. For concreteness, the presentation is focused to illustrating the oscillatory mixing effects on the periodic orbits, through which the harmonic oscillation born in a Hopf bifurcation becomes successively enriched with the intermittent incorporation of other oscillation modes of higher frequencies while the orbit remains periodic and without necessity of bifurcating instabilities. Even in the absence of a proper mathematical theory covering the nonlinear mixing mechanisms we find enough evidence to expect that the oscillatory scenario be truly scalable concerning the phase space dimension, the multiplicity of involved fixed points and the range of time scales, so that extremely complex but ordered dynamical behaviors could be sustained through it.20212021-02-0120212021-05-18reporthttp://purl.org/coar/resource_type/c_93fcAOhttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/2117/345842reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 3.0 Spainhttp://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3458422026-05-27T15:37:01Z
dc.title.none.fl_str_mv Designable Dynamical Systems for the Generalized Landau Scenario and the Nonlinear Complexification of Periodic Orbits
title Designable Dynamical Systems for the Generalized Landau Scenario and the Nonlinear Complexification of Periodic Orbits
spellingShingle Designable Dynamical Systems for the Generalized Landau Scenario and the Nonlinear Complexification of Periodic Orbits
Herrero Simon, Ramon|||0000-0001-5572-1540
Bifurcation theory
Dynamics
Bifurcació, Teoria de la
Dinàmica
Àrees temàtiques de la UPC::Física
title_short Designable Dynamical Systems for the Generalized Landau Scenario and the Nonlinear Complexification of Periodic Orbits
title_full Designable Dynamical Systems for the Generalized Landau Scenario and the Nonlinear Complexification of Periodic Orbits
title_fullStr Designable Dynamical Systems for the Generalized Landau Scenario and the Nonlinear Complexification of Periodic Orbits
title_full_unstemmed Designable Dynamical Systems for the Generalized Landau Scenario and the Nonlinear Complexification of Periodic Orbits
title_sort Designable Dynamical Systems for the Generalized Landau Scenario and the Nonlinear Complexification of Periodic Orbits
dc.creator.none.fl_str_mv Herrero Simon, Ramon|||0000-0001-5572-1540
Farjas Silva, Jordi
Pi Vila, Francesc
Orriols Tubella, Gaspar
author Herrero Simon, Ramon|||0000-0001-5572-1540
author_facet Herrero Simon, Ramon|||0000-0001-5572-1540
Farjas Silva, Jordi
Pi Vila, Francesc
Orriols Tubella, Gaspar
author_role author
author2 Farjas Silva, Jordi
Pi Vila, Francesc
Orriols Tubella, Gaspar
author2_role author
author
author
dc.subject.none.fl_str_mv Bifurcation theory
Dynamics
Bifurcació, Teoria de la
Dinàmica
Àrees temàtiques de la UPC::Física
topic Bifurcation theory
Dynamics
Bifurcació, Teoria de la
Dinàmica
Àrees temàtiques de la UPC::Física
description We have found a way for penetrating the space of the dynamical systems towards systems of arbitrary dimension exhibiting the nonlinear mixing of a large number of oscillation modes through which extraordinarily complex time evolutions arise. The system design is based on assuring the occurrence of a number of Hopf bifurcations in a set of fixed points of a relatively generic system of ordinary differential equations, in which the main peculiarity is that the nonlinearities appear through functions of a linear combination of the system variables. The paper presents the design procedure and a selection of numerical simulations with a variety of designed systems whose dynamical behaviors are really rich and full of unknown features. For concreteness, the presentation is focused to illustrating the oscillatory mixing effects on the periodic orbits, through which the harmonic oscillation born in a Hopf bifurcation becomes successively enriched with the intermittent incorporation of other oscillation modes of higher frequencies while the orbit remains periodic and without necessity of bifurcating instabilities. Even in the absence of a proper mathematical theory covering the nonlinear mixing mechanisms we find enough evidence to expect that the oscillatory scenario be truly scalable concerning the phase space dimension, the multiplicity of involved fixed points and the range of time scales, so that extremely complex but ordered dynamical behaviors could be sustained through it.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-02-01
2021
2021-05-18
dc.type.none.fl_str_mv report
http://purl.org/coar/resource_type/c_93fc
AO
http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/345842
url https://hdl.handle.net/2117/345842
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 3.0 Spain
http://creativecommons.org/licenses/by/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 3.0 Spain
http://creativecommons.org/licenses/by/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
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