Bifurcations and multistability in the extended Hindmarsh-Rose neuronal oscillator
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | , , , |
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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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 |
|
_version_ |
1808129271606018048 |