On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

dc.contributor.authorChavarette, Fábio Roberto
dc.contributor.authorBalthazar, José Manoel [UNESP]
dc.contributor.authorRafikov, Marat
dc.contributor.authorHermini, Heider Anibal
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniversidade Estadual de Campinas (UNICAMP)
dc.contributor.institutionUniversidade Regional do Noroeste do Estado do Rio Grande do Sul (Unijuí)
dc.date.accessioned2013-09-30T18:50:33Z
dc.date.accessioned2014-05-20T14:16:22Z
dc.date.available2013-09-30T18:50:33Z
dc.date.available2014-05-20T14:16:22Z
dc.date.issued2009-02-28
dc.description.abstractIn this paper, we have studied the plasmatic membrane behavior using all electric circuit developed by Hodgkin and Huxley in 1952 and have dealt with the variation of the amount of time related to the potassium and sodium conductances in the squid axon. They developed differential equations for the propagation of electric signals; the dynamics of the Hodgkin-Huxley model have been extensively studied both from the view point of its their biological implications and as a test bed for numerical methods, which can be applied to more complex models. Recently, all irregular chaotic movement of the action potential of the membrane was observed for a number of techniques of control with the objective to stabilize the variation of this potential. This paper analyzes the non-linear dynamics of the Hodgkin-Huxley mathematical model, and we present some modifications in the governing equations of the system in order to make it a non-ideal one (taking into account that the energy source has a limited power supply). We also developed an optimal linear control design for the action potential of membranes. Here, we discuss the conditions that allow the use of control linear feedback for this kind of non-linear system.en
dc.description.affiliationState Univ São Paulo Rio Claro, BR-13500230 Rio Claro, SP, Brazil
dc.description.affiliationUniv Estadual Campinas, Dept Mech Design, BR-13083970 Campinas, SP, Brazil
dc.description.affiliationUniv Reg Noroeste Estado Rio Grande do Sul, BR-98700000 Ijui, RS, Brazil
dc.description.affiliationUnespState Univ São Paulo Rio Claro, BR-13500230 Rio Claro, SP, Brazil
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.format.extent1651-1666
dc.identifierhttp://dx.doi.org/10.1016/j.chaos.2007.06.016
dc.identifier.citationChaos Solitons & Fractals. Oxford: Pergamon-Elsevier B.V. Ltd, v. 39, n. 4, p. 1651-1666, 2009.
dc.identifier.doi10.1016/j.chaos.2007.06.016
dc.identifier.issn0960-0779
dc.identifier.lattes5723359885365339
dc.identifier.orcid0000-0002-1203-7586
dc.identifier.urihttp://hdl.handle.net/11449/24933
dc.identifier.wosWOS:000265712000018
dc.language.isoeng
dc.publisherPergamon-Elsevier B.V. Ltd
dc.relation.ispartofChaos Solitons & Fractals
dc.relation.ispartofjcr2.213
dc.relation.ispartofsjr0,678
dc.rights.accessRightsAcesso restrito
dc.sourceWeb of Science
dc.titleOn non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical modelen
dc.typeArtigo
dcterms.licensehttp://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy
dcterms.rightsHolderPergamon-Elsevier B.V. Ltd
unesp.author.lattes5723359885365339(1)
unesp.author.orcid0000-0002-1203-7586(1)
unesp.campusUniversidade Estadual Paulista (Unesp), Instituto de Geociências e Ciências Exatas, Rio Claropt
unesp.campusUniversidade Estadual Paulista (Unesp), Faculdade de Engenharia, Ilha Solteirapt
unesp.departmentMatemática - FEISEstatística, Matemática Aplicada e Computação - IGCEpt

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