An integro-differential equation for dynamical systems with diffusion-mediated coupling

Detalhes bibliográficos
Autor(a) principal: Aristides, Raul P. [UNESP]
Data de Publicação: 2020
Outros Autores: Viana, Ricardo L.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/s11071-020-05700-9
http://hdl.handle.net/11449/196970
Resumo: Many systems of biological interest can be modeled as pointlike oscillators whose coupling is mediated by the diffusion of some substance. This coupling occurs because the dynamics of each oscillator is influenced by the local concentration of a substance which diffuses through the spatial medium. The diffusion equation, on its hand, has a source term which depends on the oscillator dynamics. We derive a mathematical model for such a system and obtain an integro-differential equation. Its solution can be obtained by an approximation scheme for which the unperturbed solution is used to obtain a first-order solution to the coupled oscillators and so on. We present numerical results for the special case of a one-dimensional bounded domain in which the oscillators are randomly placed. Our results show the influence of the coupling parameters on some aspects of the dynamics of the coupled oscillators, like phase and frequency synchronization.
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spelling An integro-differential equation for dynamical systems with diffusion-mediated couplingOscillator couplingSynchronizationDiffusion equationMany systems of biological interest can be modeled as pointlike oscillators whose coupling is mediated by the diffusion of some substance. This coupling occurs because the dynamics of each oscillator is influenced by the local concentration of a substance which diffuses through the spatial medium. The diffusion equation, on its hand, has a source term which depends on the oscillator dynamics. We derive a mathematical model for such a system and obtain an integro-differential equation. Its solution can be obtained by an approximation scheme for which the unperturbed solution is used to obtain a first-order solution to the coupled oscillators and so on. We present numerical results for the special case of a one-dimensional bounded domain in which the oscillators are randomly placed. Our results show the influence of the coupling parameters on some aspects of the dynamics of the coupled oscillators, like phase and frequency synchronization.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Univ Fed Parana, Dept Fis, Curitiba, Parana, BrazilUniv Estadual Paulista, Inst Fis Teor, Sao Paulo, SP, BrazilUniv Estadual Paulista, Inst Fis Teor, Sao Paulo, SP, BrazilCNPq: 301019/2019-3SpringerUniv Fed ParanaUniversidade Estadual Paulista (Unesp)Aristides, Raul P. [UNESP]Viana, Ricardo L.2020-12-10T20:02:06Z2020-12-10T20:02:06Z2020-06-09info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article3759-3770http://dx.doi.org/10.1007/s11071-020-05700-9Nonlinear Dynamics. Dordrecht: Springer, v. 100, n. 4, p. 3759-3770, 2020.0924-090Xhttp://hdl.handle.net/11449/19697010.1007/s11071-020-05700-9WOS:000539177900002Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengNonlinear Dynamicsinfo:eu-repo/semantics/openAccess2021-10-23T08:46:45Zoai:repositorio.unesp.br:11449/196970Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T15:43:36.295561Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv An integro-differential equation for dynamical systems with diffusion-mediated coupling
title An integro-differential equation for dynamical systems with diffusion-mediated coupling
spellingShingle An integro-differential equation for dynamical systems with diffusion-mediated coupling
Aristides, Raul P. [UNESP]
Oscillator coupling
Synchronization
Diffusion equation
title_short An integro-differential equation for dynamical systems with diffusion-mediated coupling
title_full An integro-differential equation for dynamical systems with diffusion-mediated coupling
title_fullStr An integro-differential equation for dynamical systems with diffusion-mediated coupling
title_full_unstemmed An integro-differential equation for dynamical systems with diffusion-mediated coupling
title_sort An integro-differential equation for dynamical systems with diffusion-mediated coupling
author Aristides, Raul P. [UNESP]
author_facet Aristides, Raul P. [UNESP]
Viana, Ricardo L.
author_role author
author2 Viana, Ricardo L.
author2_role author
dc.contributor.none.fl_str_mv Univ Fed Parana
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Aristides, Raul P. [UNESP]
Viana, Ricardo L.
dc.subject.por.fl_str_mv Oscillator coupling
Synchronization
Diffusion equation
topic Oscillator coupling
Synchronization
Diffusion equation
description Many systems of biological interest can be modeled as pointlike oscillators whose coupling is mediated by the diffusion of some substance. This coupling occurs because the dynamics of each oscillator is influenced by the local concentration of a substance which diffuses through the spatial medium. The diffusion equation, on its hand, has a source term which depends on the oscillator dynamics. We derive a mathematical model for such a system and obtain an integro-differential equation. Its solution can be obtained by an approximation scheme for which the unperturbed solution is used to obtain a first-order solution to the coupled oscillators and so on. We present numerical results for the special case of a one-dimensional bounded domain in which the oscillators are randomly placed. Our results show the influence of the coupling parameters on some aspects of the dynamics of the coupled oscillators, like phase and frequency synchronization.
publishDate 2020
dc.date.none.fl_str_mv 2020-12-10T20:02:06Z
2020-12-10T20:02:06Z
2020-06-09
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1007/s11071-020-05700-9
Nonlinear Dynamics. Dordrecht: Springer, v. 100, n. 4, p. 3759-3770, 2020.
0924-090X
http://hdl.handle.net/11449/196970
10.1007/s11071-020-05700-9
WOS:000539177900002
url http://dx.doi.org/10.1007/s11071-020-05700-9
http://hdl.handle.net/11449/196970
identifier_str_mv Nonlinear Dynamics. Dordrecht: Springer, v. 100, n. 4, p. 3759-3770, 2020.
0924-090X
10.1007/s11071-020-05700-9
WOS:000539177900002
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Nonlinear Dynamics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 3759-3770
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv Web of Science
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808128553793880064

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