Lyapunov exponents and extensivity of strongly coupled chaotic maps in regular graphs

n Thermodynamics and Statistical Physics, a system’s property is extensive when it grows with the system size. When it happens, the system can be decomposed into separate components, which has been done in many systems with weakly interacting components, such as for various gas models. Similarly, Ru...

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Detalles Bibliográficos
Autores: Gancio Vázquez, Juan, Rubido, Nicolas
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:español
OAI Identifier:oai:upcommons.upc.edu:2117/399111
Acceso en línea:https://hdl.handle.net/2117/399111
https://dx.doi.org/10.1016/j.chaos.2023.114392
Access Level:acceso abierto
Palabra clave:Coupled map lattices
Lyapunov exponents
Coupled maps
Regular graphs
Extensivity
Lyapunov, Exponents de
Àrees temàtiques de la UPC::Física
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spelling Lyapunov exponents and extensivity of strongly coupled chaotic maps in regular graphsGancio Vázquez, JuanRubido, NicolasCoupled map latticesLyapunov exponentsCoupled mapsRegular graphsExtensivityLyapunov exponentsLyapunov, Exponents deÀrees temàtiques de la UPC::Físican Thermodynamics and Statistical Physics, a system’s property is extensive when it grows with the system size. When it happens, the system can be decomposed into separate components, which has been done in many systems with weakly interacting components, such as for various gas models. Similarly, Ruelle conjectured 40 years ago that the Lyapunov exponents (LEs) of some sufficiently large chaotic systems are extensive, which led to study the extensivity properties of chaotic systems with strong interactions. Because of the complexities in these systems, most results achieved so far are restricted to numerical simulations. Here, we derive closed-form expressions for the LEs and entropy rate of coupled maps in finite- and infinite-sized regular graphs, according to the coupling strength, map’s chaoticity, and graph’s spectral properties. We show that this type of system has either 4 or 5 cases for the LEs, depending on the graph’s extreme Laplacian eigenvalues. These cases represent qualitatively different collective behaviours emerging in parameter space, including chaotic synchronisation (negative LEs) and incoherent chaos ( positive LEs). From the entropy rate, we show that the ring and complete graphs (nearest-neighbour and all-to-all couplings, respectively) are extensive in all parameter regions outside the chaotic synchronisation region. Although our derivations are restricted to one-dimensional maps with constant positive derivative (i.e., chaotic), our approach can be used to find LE and entropy rates for other regular graphs (such as for cyclic graphs) or be the basis for tackling small world graphs via perturbative methods.J.G. acknowledges funds from the Agencia Nacional de Investigación e Innonvación (ANII), Uruguay, POS_NAC_2018_1_151185, and the Comisión Academica de Posgrado (CAP), Universidad de la República, Uruguay. Both authors acknowledge funds from the Comisión Sectorial de Investigación Cientifíca (CSIC), Uruguay, group grant “CSIC2018 - FID13 - grupo ID 722 ”.Peer ReviewedElsevier20242024-01-0120242024-01-10journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/399111https://dx.doi.org/10.1016/j.chaos.2023.114392reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Españolspaopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3991112026-05-27T15:37:01Z
dc.title.none.fl_str_mv Lyapunov exponents and extensivity of strongly coupled chaotic maps in regular graphs
title Lyapunov exponents and extensivity of strongly coupled chaotic maps in regular graphs
spellingShingle Lyapunov exponents and extensivity of strongly coupled chaotic maps in regular graphs
Gancio Vázquez, Juan
Coupled map lattices
Lyapunov exponents
Coupled maps
Regular graphs
Extensivity
Lyapunov exponents
Lyapunov, Exponents de
Àrees temàtiques de la UPC::Física
title_short Lyapunov exponents and extensivity of strongly coupled chaotic maps in regular graphs
title_full Lyapunov exponents and extensivity of strongly coupled chaotic maps in regular graphs
title_fullStr Lyapunov exponents and extensivity of strongly coupled chaotic maps in regular graphs
title_full_unstemmed Lyapunov exponents and extensivity of strongly coupled chaotic maps in regular graphs
title_sort Lyapunov exponents and extensivity of strongly coupled chaotic maps in regular graphs
dc.creator.none.fl_str_mv Gancio Vázquez, Juan
Rubido, Nicolas
author Gancio Vázquez, Juan
author_facet Gancio Vázquez, Juan
Rubido, Nicolas
author_role author
author2 Rubido, Nicolas
author2_role author
dc.subject.none.fl_str_mv Coupled map lattices
Lyapunov exponents
Coupled maps
Regular graphs
Extensivity
Lyapunov exponents
Lyapunov, Exponents de
Àrees temàtiques de la UPC::Física
topic Coupled map lattices
Lyapunov exponents
Coupled maps
Regular graphs
Extensivity
Lyapunov exponents
Lyapunov, Exponents de
Àrees temàtiques de la UPC::Física
description n Thermodynamics and Statistical Physics, a system’s property is extensive when it grows with the system size. When it happens, the system can be decomposed into separate components, which has been done in many systems with weakly interacting components, such as for various gas models. Similarly, Ruelle conjectured 40 years ago that the Lyapunov exponents (LEs) of some sufficiently large chaotic systems are extensive, which led to study the extensivity properties of chaotic systems with strong interactions. Because of the complexities in these systems, most results achieved so far are restricted to numerical simulations. Here, we derive closed-form expressions for the LEs and entropy rate of coupled maps in finite- and infinite-sized regular graphs, according to the coupling strength, map’s chaoticity, and graph’s spectral properties. We show that this type of system has either 4 or 5 cases for the LEs, depending on the graph’s extreme Laplacian eigenvalues. These cases represent qualitatively different collective behaviours emerging in parameter space, including chaotic synchronisation (negative LEs) and incoherent chaos ( positive LEs). From the entropy rate, we show that the ring and complete graphs (nearest-neighbour and all-to-all couplings, respectively) are extensive in all parameter regions outside the chaotic synchronisation region. Although our derivations are restricted to one-dimensional maps with constant positive derivative (i.e., chaotic), our approach can be used to find LE and entropy rates for other regular graphs (such as for cyclic graphs) or be the basis for tackling small world graphs via perturbative methods.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-01-01
2024
2024-01-10
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/399111
https://dx.doi.org/10.1016/j.chaos.2023.114392
url https://hdl.handle.net/2117/399111
https://dx.doi.org/10.1016/j.chaos.2023.114392
dc.language.none.fl_str_mv Español
spa
language_invalid_str_mv Español
language spa
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
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-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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