On the analytical solutions of the Hindmarsh-Rose neuronal model

Detalhes bibliográficos
Autor(a) principal: Duarte, Jorge
Data de Publicação: 2015
Outros Autores: Januário, Cristina, Martins, Nuno
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.21/5997
Resumo: In this article we analytically solve the Hindmarsh-Rose model (Proc R Soc Lond B221:87-102, 1984) by means of a technique developed for strongly nonlinear problems-the step homotopy analysis method. This analytical algorithm, based on a modification of the standard homotopy analysis method, allows us to obtain a one-parameter family of explicit series solutions for the studied neuronal model. The Hindmarsh-Rose system represents a paradigmatic example of models developed to qualitatively reproduce the electrical activity of cell membranes. By using the homotopy solutions, we investigate the dynamical effect of two chosen biologically meaningful bifurcation parameters: the injected current I and the parameter r, representing the ratio of time scales between spiking (fast dynamics) and resting (slow dynamics). The auxiliary parameter involved in the analytical method provides us with an elegant way to ensure convergent series solutions of the neuronal model. Our analytical results are found to be in excellent agreement with the numerical simulations.
id RCAP_87cfae639601ca524c414cdc2135f082
oai_identifier_str oai:repositorio.ipl.pt:10400.21/5997
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling On the analytical solutions of the Hindmarsh-Rose neuronal modelAnalytic solutionsNonlinear differential equationsChaosNeuronal modelHomotopy analysis methodStep homotopy analysis methodIn this article we analytically solve the Hindmarsh-Rose model (Proc R Soc Lond B221:87-102, 1984) by means of a technique developed for strongly nonlinear problems-the step homotopy analysis method. This analytical algorithm, based on a modification of the standard homotopy analysis method, allows us to obtain a one-parameter family of explicit series solutions for the studied neuronal model. The Hindmarsh-Rose system represents a paradigmatic example of models developed to qualitatively reproduce the electrical activity of cell membranes. By using the homotopy solutions, we investigate the dynamical effect of two chosen biologically meaningful bifurcation parameters: the injected current I and the parameter r, representing the ratio of time scales between spiking (fast dynamics) and resting (slow dynamics). The auxiliary parameter involved in the analytical method provides us with an elegant way to ensure convergent series solutions of the neuronal model. Our analytical results are found to be in excellent agreement with the numerical simulations.SPRINGERRCIPLDuarte, JorgeJanuário, CristinaMartins, Nuno2016-04-15T14:07:59Z2015-112015-11-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/5997engDUARTE, JORGE; JANUÁRIO,CRISTINA; MARTINS, NUNO - On the analytical solutions of the Hindmarsh-Rose neuronal model. Nonlinear Dynamics. ISSN. 0924-090X. Vol. 82, N.º 3 (2015), pp. 1221-12310924-090X10.1007/s11071-015-2228-5metadata only accessinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-08-03T09:50:14Zoai:repositorio.ipl.pt:10400.21/5997Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:15:12.700661Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv On the analytical solutions of the Hindmarsh-Rose neuronal model
title On the analytical solutions of the Hindmarsh-Rose neuronal model
spellingShingle On the analytical solutions of the Hindmarsh-Rose neuronal model
Duarte, Jorge
Analytic solutions
Nonlinear differential equations
Chaos
Neuronal model
Homotopy analysis method
Step homotopy analysis method
title_short On the analytical solutions of the Hindmarsh-Rose neuronal model
title_full On the analytical solutions of the Hindmarsh-Rose neuronal model
title_fullStr On the analytical solutions of the Hindmarsh-Rose neuronal model
title_full_unstemmed On the analytical solutions of the Hindmarsh-Rose neuronal model
title_sort On the analytical solutions of the Hindmarsh-Rose neuronal model
author Duarte, Jorge
author_facet Duarte, Jorge
Januário, Cristina
Martins, Nuno
author_role author
author2 Januário, Cristina
Martins, Nuno
author2_role author
author
dc.contributor.none.fl_str_mv RCIPL
dc.contributor.author.fl_str_mv Duarte, Jorge
Januário, Cristina
Martins, Nuno
dc.subject.por.fl_str_mv Analytic solutions
Nonlinear differential equations
Chaos
Neuronal model
Homotopy analysis method
Step homotopy analysis method
topic Analytic solutions
Nonlinear differential equations
Chaos
Neuronal model
Homotopy analysis method
Step homotopy analysis method
description In this article we analytically solve the Hindmarsh-Rose model (Proc R Soc Lond B221:87-102, 1984) by means of a technique developed for strongly nonlinear problems-the step homotopy analysis method. This analytical algorithm, based on a modification of the standard homotopy analysis method, allows us to obtain a one-parameter family of explicit series solutions for the studied neuronal model. The Hindmarsh-Rose system represents a paradigmatic example of models developed to qualitatively reproduce the electrical activity of cell membranes. By using the homotopy solutions, we investigate the dynamical effect of two chosen biologically meaningful bifurcation parameters: the injected current I and the parameter r, representing the ratio of time scales between spiking (fast dynamics) and resting (slow dynamics). The auxiliary parameter involved in the analytical method provides us with an elegant way to ensure convergent series solutions of the neuronal model. Our analytical results are found to be in excellent agreement with the numerical simulations.
publishDate 2015
dc.date.none.fl_str_mv 2015-11
2015-11-01T00:00:00Z
2016-04-15T14:07:59Z
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://hdl.handle.net/10400.21/5997
url http://hdl.handle.net/10400.21/5997
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv DUARTE, JORGE; JANUÁRIO,CRISTINA; MARTINS, NUNO - On the analytical solutions of the Hindmarsh-Rose neuronal model. Nonlinear Dynamics. ISSN. 0924-090X. Vol. 82, N.º 3 (2015), pp. 1221-1231
0924-090X
10.1007/s11071-015-2228-5
dc.rights.driver.fl_str_mv metadata only access
info:eu-repo/semantics/openAccess
rights_invalid_str_mv metadata only access
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv SPRINGER
publisher.none.fl_str_mv SPRINGER
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
_version_ 1799133409821327360

Registros relacionados