An integro-differential equation for dynamical systems with diffusion-mediated coupling
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | |
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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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 |