Bifurcations and multistability in the extended Hindmarsh-Rose neuronal oscillator

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dc.contributor.authorMegam Ngouonkadi, E. B.
dc.contributor.authorFotsin, H. B.
dc.contributor.authorLouodop Fotso, P. [UNESP]
dc.contributor.authorKamdoum Tamba, V.
dc.contributor.authorCerdeira, Hilda A. [UNESP]
dc.contributor.institutionUniversity of Dschang
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2018-12-11T17:01:25Z
dc.date.available2018-12-11T17:01:25Z
dc.date.issued2016-04-01
dc.description.abstractWe report on the bifurcation analysis of an extended Hindmarsh-Rose (eHR) neuronal oscillator. We prove that Hopf bifurcation occurs in this system, when an appropriate chosen bifurcation parameter varies and reaches its critical value. Applying the normal form theory, we derive a formula to determine the direction of the Hopf bifurcation and the stability of bifurcating periodic flows. To observe this latter bifurcation and to illustrate its theoretical analysis, numerical simulations are performed. Hence, we present an explanation of the discontinuous behavior of the amplitude of the repetitive response as a function of system's parameters based on the presence of the subcritical unstable oscillations. Furthermore, the bifurcation structures of the system are studied, with special care on the effects of parameters associated with the slow current and the slower dynamical process. We find that the system presents diversity of bifurcations such as period-doubling, symmetry breaking, crises and reverse period-doubling, when the afore mentioned parameters are varied in tiny steps. The complexity of the bifurcation structures seems useful to understand how neurons encode information or how they respond to external stimuli. Furthermore, we find that the extended Hindmarsh-Rose model also presents the multistability of oscillatory and silent regimes for precise sets of its parameters. This phenomenon plays a practical role in short-term memory and appears to give an evolutionary advantage for neurons since they constitute part of multifunctional microcircuits such as central pattern generators.en
dc.description.affiliationLaboratory of Electronics and Signal Processing Department of Physics Faculty of Sciences University of Dschang, P.O. Box 067
dc.description.affiliationInstituto de Física Teórica UNESP Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271,Bloco II
dc.description.affiliationUnespInstituto de Física Teórica UNESP Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271,Bloco II
dc.format.extent151-163
dc.identifierhttp://dx.doi.org/10.1016/j.chaos.2016.02.001
dc.identifier.citationChaos, Solitons and Fractals, v. 85, p. 151-163.
dc.identifier.doi10.1016/j.chaos.2016.02.001
dc.identifier.file2-s2.0-84959365997.pdf
dc.identifier.issn0960-0779
dc.identifier.scopus2-s2.0-84959365997
dc.identifier.urihttp://hdl.handle.net/11449/172607
dc.language.isoeng
dc.relation.ispartofChaos, Solitons and Fractals
dc.relation.ispartofsjr0,678
dc.rights.accessRightsAcesso aberto
dc.sourceScopus
dc.subjectBifurcation diagram
dc.subjectCrisis
dc.subjectHindmarsh-Rose oscillator
dc.subjectHopf bifurcation
dc.subjectMultistability
dc.subjectPeriodic solution
dc.titleBifurcations and multistability in the extended Hindmarsh-Rose neuronal oscillatoren
dc.typeArtigo
unesp.author.orcid0000-0003-4805-4668[5]

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