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On the analytical solutions of the Hindmarsh-Rose neuronal model

2015-11Journal article Restricted access
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dc.contributor.authorDuarte, Jorge
dc.contributor.authorJanuário, Cristina
dc.contributor.authorMartins, Nuno
dc.date.accessioned2016-04-15T14:07:59Z
dc.date.available2016-04-15T14:07:59Z
dc.date.issued2015-11
dc.description.abstractIn 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.pt_PT
dc.identifier.citationDUARTE, 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. 1221-1231pt_PT
dc.identifier.doi10.1007/s11071-015-2228-5pt_PT
dc.identifier.issn0924-090X
dc.identifier.issn1573-269X
dc.identifier.urihttp://hdl.handle.net/10400.21/5997
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherSPRINGERpt_PT
dc.relation.publisherversionhttp://link.springer.com/article/10.1007/s11071-015-2228-5pt_PT
dc.subjectAnalytic solutionspt_PT
dc.subjectNonlinear differential equationspt_PT
dc.subjectChaospt_PT
dc.subjectNeuronal modelpt_PT
dc.subjectHomotopy analysis methodpt_PT
dc.subjectStep homotopy analysis methodpt_PT
dc.titleOn the analytical solutions of the Hindmarsh-Rose neuronal modelpt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/3599-PPCDT/PEst-OE%2FEEI%2FLA0009%2F2013/PT
oaire.citation.endPage1231pt_PT
oaire.citation.issue3pt_PT
oaire.citation.startPage1221pt_PT
oaire.citation.volume82pt_PT
oaire.fundingStream3599-PPCDT
person.familyNameDuarte
person.familyNameJanuário
person.givenNameJorge
person.givenNameCristina
person.identifier.ciencia-idBC1D-1E83-E2B2
person.identifier.orcid0000-0003-2641-3199
person.identifier.orcid0000-0002-6978-876X
person.identifier.ridG-7261-2011
person.identifier.scopus-author-id35310049800
person.identifier.scopus-author-id56526791400
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT
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relation.isAuthorOfPublication42a4023b-b4c4-4456-aaba-d97bf8c14d6a
relation.isAuthorOfPublication.latestForDiscovery42a4023b-b4c4-4456-aaba-d97bf8c14d6a
relation.isProjectOfPublication9e152db9-9776-4b55-aedf-203a6dc11d8a
relation.isProjectOfPublication.latestForDiscovery9e152db9-9776-4b55-aedf-203a6dc11d8a

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