Bifurcations and multistability in the extended Hindmarsh-Rose neuronal oscillator

Detalhes bibliográficos
Autor(a) principal: Megam Ngouonkadi, E. B.
Data de Publicação: 2016
Outros Autores: Fotsin, H. B., Louodop Fotso, P. [UNESP], Kamdoum Tamba, V., Cerdeira, Hilda A. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.chaos.2016.02.001
http://hdl.handle.net/11449/172607
Resumo: We 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.
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spelling Bifurcations and multistability in the extended Hindmarsh-Rose neuronal oscillatorBifurcation diagramCrisisHindmarsh-Rose oscillatorHopf bifurcationMultistabilityPeriodic solutionWe 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.Laboratory of Electronics and Signal Processing Department of Physics Faculty of Sciences University of Dschang, P.O. Box 067Instituto de Física Teórica UNESP Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271,Bloco IIInstituto de Física Teórica UNESP Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271,Bloco IIUniversity of DschangUniversidade Estadual Paulista (Unesp)Megam Ngouonkadi, E. B.Fotsin, H. B.Louodop Fotso, P. [UNESP]Kamdoum Tamba, V.Cerdeira, Hilda A. [UNESP]2018-12-11T17:01:25Z2018-12-11T17:01:25Z2016-04-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article151-163application/pdfhttp://dx.doi.org/10.1016/j.chaos.2016.02.001Chaos, Solitons and Fractals, v. 85, p. 151-163.0960-0779http://hdl.handle.net/11449/17260710.1016/j.chaos.2016.02.0012-s2.0-849593659972-s2.0-84959365997.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengChaos, Solitons and Fractals0,678info:eu-repo/semantics/openAccess2023-12-22T06:21:08Zoai:repositorio.unesp.br:11449/172607Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T20:59:38.094972Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Bifurcations and multistability in the extended Hindmarsh-Rose neuronal oscillator
title Bifurcations and multistability in the extended Hindmarsh-Rose neuronal oscillator
spellingShingle Bifurcations and multistability in the extended Hindmarsh-Rose neuronal oscillator
Megam Ngouonkadi, E. B.
Bifurcation diagram
Crisis
Hindmarsh-Rose oscillator
Hopf bifurcation
Multistability
Periodic solution
title_short Bifurcations and multistability in the extended Hindmarsh-Rose neuronal oscillator
title_full Bifurcations and multistability in the extended Hindmarsh-Rose neuronal oscillator
title_fullStr Bifurcations and multistability in the extended Hindmarsh-Rose neuronal oscillator
title_full_unstemmed Bifurcations and multistability in the extended Hindmarsh-Rose neuronal oscillator
title_sort Bifurcations and multistability in the extended Hindmarsh-Rose neuronal oscillator
author Megam Ngouonkadi, E. B.
author_facet Megam Ngouonkadi, E. B.
Fotsin, H. B.
Louodop Fotso, P. [UNESP]
Kamdoum Tamba, V.
Cerdeira, Hilda A. [UNESP]
author_role author
author2 Fotsin, H. B.
Louodop Fotso, P. [UNESP]
Kamdoum Tamba, V.
Cerdeira, Hilda A. [UNESP]
author2_role author
author
author
author
dc.contributor.none.fl_str_mv University of Dschang
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Megam Ngouonkadi, E. B.
Fotsin, H. B.
Louodop Fotso, P. [UNESP]
Kamdoum Tamba, V.
Cerdeira, Hilda A. [UNESP]
dc.subject.por.fl_str_mv Bifurcation diagram
Crisis
Hindmarsh-Rose oscillator
Hopf bifurcation
Multistability
Periodic solution
topic Bifurcation diagram
Crisis
Hindmarsh-Rose oscillator
Hopf bifurcation
Multistability
Periodic solution
description We 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.
publishDate 2016
dc.date.none.fl_str_mv 2016-04-01
2018-12-11T17:01:25Z
2018-12-11T17:01:25Z
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://dx.doi.org/10.1016/j.chaos.2016.02.001
Chaos, Solitons and Fractals, v. 85, p. 151-163.
0960-0779
http://hdl.handle.net/11449/172607
10.1016/j.chaos.2016.02.001
2-s2.0-84959365997
2-s2.0-84959365997.pdf
url http://dx.doi.org/10.1016/j.chaos.2016.02.001
http://hdl.handle.net/11449/172607
identifier_str_mv Chaos, Solitons and Fractals, v. 85, p. 151-163.
0960-0779
10.1016/j.chaos.2016.02.001
2-s2.0-84959365997
2-s2.0-84959365997.pdf
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Chaos, Solitons and Fractals
0,678
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 151-163
application/pdf
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
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