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.author | Chavarette, Fábio Roberto | |
dc.contributor.author | Balthazar, José Manoel [UNESP] | |
dc.contributor.author | Rafikov, Marat | |
dc.contributor.author | Hermini, Heider Anibal | |
dc.contributor.institution | Universidade Estadual Paulista (Unesp) | |
dc.contributor.institution | Universidade Estadual de Campinas (UNICAMP) | |
dc.contributor.institution | Universidade Regional do Noroeste do Estado do Rio Grande do Sul (Unijuí) | |
dc.date.accessioned | 2013-09-30T18:50:33Z | |
dc.date.accessioned | 2014-05-20T14:16:22Z | |
dc.date.available | 2013-09-30T18:50:33Z | |
dc.date.available | 2014-05-20T14:16:22Z | |
dc.date.issued | 2009-02-28 | |
dc.description.abstract | In 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.affiliation | State Univ São Paulo Rio Claro, BR-13500230 Rio Claro, SP, Brazil | |
dc.description.affiliation | Univ Estadual Campinas, Dept Mech Design, BR-13083970 Campinas, SP, Brazil | |
dc.description.affiliation | Univ Reg Noroeste Estado Rio Grande do Sul, BR-98700000 Ijui, RS, Brazil | |
dc.description.affiliationUnesp | State Univ São Paulo Rio Claro, BR-13500230 Rio Claro, SP, Brazil | |
dc.description.sponsorship | Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) | |
dc.description.sponsorship | Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) | |
dc.format.extent | 1651-1666 | |
dc.identifier | http://dx.doi.org/10.1016/j.chaos.2007.06.016 | |
dc.identifier.citation | Chaos Solitons & Fractals. Oxford: Pergamon-Elsevier B.V. Ltd, v. 39, n. 4, p. 1651-1666, 2009. | |
dc.identifier.doi | 10.1016/j.chaos.2007.06.016 | |
dc.identifier.issn | 0960-0779 | |
dc.identifier.lattes | 5723359885365339 | |
dc.identifier.orcid | 0000-0002-1203-7586 | |
dc.identifier.uri | http://hdl.handle.net/11449/24933 | |
dc.identifier.wos | WOS:000265712000018 | |
dc.language.iso | eng | |
dc.publisher | Pergamon-Elsevier B.V. Ltd | |
dc.relation.ispartof | Chaos Solitons & Fractals | |
dc.relation.ispartofjcr | 2.213 | |
dc.relation.ispartofsjr | 0,678 | |
dc.rights.accessRights | Acesso restrito | |
dc.source | Web of Science | |
dc.title | 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 | en |
dc.type | Artigo | |
dcterms.license | http://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy | |
dcterms.rightsHolder | Pergamon-Elsevier B.V. Ltd | |
unesp.author.lattes | 5723359885365339(1) | |
unesp.author.orcid | 0000-0002-1203-7586(1) | |
unesp.campus | Universidade Estadual Paulista (Unesp), Instituto de Geociências e Ciências Exatas, Rio Claro | pt |
unesp.campus | Universidade Estadual Paulista (Unesp), Faculdade de Engenharia, Ilha Solteira | pt |
unesp.department | Matemática - FEISEstatística, Matemática Aplicada e Computação - IGCE | pt |
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