Nonlinear Dynamics, Chaos and Control of the Hindmarsh-Rose Neuron Model

Detalhes bibliográficos
Autor(a) principal: de Lima, Raildo Santos
Data de Publicação: 2022
Outros Autores: Chavarette, Fábio Roberto [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.5269/bspm.47770
http://hdl.handle.net/11449/234102
Resumo: Mathematics has changed over time to comprise interdisciplinary fields of research, and consid- ering this, biomathematics has arisen as an interface study. In this work, we analyze the dynamical behavior of the Hindmarsh-Rose neuron model, which describes the neuronal bursting in a single neuron. A stability study through the Lyapunov exponents method is proposed and evidence of a chaotic dynamics is presented. This chaotic behavior is biologically comparable to an individual undergoing an epileptic seizure, in which the application of an efficient controller represents a proposal for preventing epilepsy from happening. Therefore, a control design based on the State-Dependent Riccati Equation is proposed aiming to reduce the oscillation of the system to a desired orbit. The results show that the controller is efficient and robust as a method for preventing epileptic seizures.
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spelling Nonlinear Dynamics, Chaos and Control of the Hindmarsh-Rose Neuron ModelChaosnonlinear dynamicssdre controlMathematics has changed over time to comprise interdisciplinary fields of research, and consid- ering this, biomathematics has arisen as an interface study. In this work, we analyze the dynamical behavior of the Hindmarsh-Rose neuron model, which describes the neuronal bursting in a single neuron. A stability study through the Lyapunov exponents method is proposed and evidence of a chaotic dynamics is presented. This chaotic behavior is biologically comparable to an individual undergoing an epileptic seizure, in which the application of an efficient controller represents a proposal for preventing epilepsy from happening. Therefore, a control design based on the State-Dependent Riccati Equation is proposed aiming to reduce the oscillation of the system to a desired orbit. The results show that the controller is efficient and robust as a method for preventing epileptic seizures.Department of Mathematics UFMS - Universidade Federal de Mato Grosso do SulDepartment of Mathematics UNESP - Universidade Estadual Pauslita Julio de Mesquita FilhoDepartment of Mathematics UNESP - Universidade Estadual Pauslita Julio de Mesquita FilhoUniversidade Federal de Mato Grosso do Sul (UFMS)Universidade Estadual Paulista (UNESP)de Lima, Raildo SantosChavarette, Fábio Roberto [UNESP]2022-05-01T13:41:28Z2022-05-01T13:41:28Z2022-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.5269/bspm.47770Boletim da Sociedade Paranaense de Matematica, v. 40.2175-11880037-8712http://hdl.handle.net/11449/23410210.5269/bspm.477702-s2.0-85124081366Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengBoletim da Sociedade Paranaense de Matematicainfo:eu-repo/semantics/openAccess2024-07-10T15:41:35Zoai:repositorio.unesp.br:11449/234102Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T13:42:30.120706Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Nonlinear Dynamics, Chaos and Control of the Hindmarsh-Rose Neuron Model
title Nonlinear Dynamics, Chaos and Control of the Hindmarsh-Rose Neuron Model
spellingShingle Nonlinear Dynamics, Chaos and Control of the Hindmarsh-Rose Neuron Model
de Lima, Raildo Santos
Chaos
nonlinear dynamics
sdre control
title_short Nonlinear Dynamics, Chaos and Control of the Hindmarsh-Rose Neuron Model
title_full Nonlinear Dynamics, Chaos and Control of the Hindmarsh-Rose Neuron Model
title_fullStr Nonlinear Dynamics, Chaos and Control of the Hindmarsh-Rose Neuron Model
title_full_unstemmed Nonlinear Dynamics, Chaos and Control of the Hindmarsh-Rose Neuron Model
title_sort Nonlinear Dynamics, Chaos and Control of the Hindmarsh-Rose Neuron Model
author de Lima, Raildo Santos
author_facet de Lima, Raildo Santos
Chavarette, Fábio Roberto [UNESP]
author_role author
author2 Chavarette, Fábio Roberto [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade Federal de Mato Grosso do Sul (UFMS)
Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv de Lima, Raildo Santos
Chavarette, Fábio Roberto [UNESP]
dc.subject.por.fl_str_mv Chaos
nonlinear dynamics
sdre control
topic Chaos
nonlinear dynamics
sdre control
description Mathematics has changed over time to comprise interdisciplinary fields of research, and consid- ering this, biomathematics has arisen as an interface study. In this work, we analyze the dynamical behavior of the Hindmarsh-Rose neuron model, which describes the neuronal bursting in a single neuron. A stability study through the Lyapunov exponents method is proposed and evidence of a chaotic dynamics is presented. This chaotic behavior is biologically comparable to an individual undergoing an epileptic seizure, in which the application of an efficient controller represents a proposal for preventing epilepsy from happening. Therefore, a control design based on the State-Dependent Riccati Equation is proposed aiming to reduce the oscillation of the system to a desired orbit. The results show that the controller is efficient and robust as a method for preventing epileptic seizures.
publishDate 2022
dc.date.none.fl_str_mv 2022-05-01T13:41:28Z
2022-05-01T13:41:28Z
2022-01-01
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/10.5269/bspm.47770
Boletim da Sociedade Paranaense de Matematica, v. 40.
2175-1188
0037-8712
http://hdl.handle.net/11449/234102
10.5269/bspm.47770
2-s2.0-85124081366
url http://dx.doi.org/10.5269/bspm.47770
http://hdl.handle.net/11449/234102
identifier_str_mv Boletim da Sociedade Paranaense de Matematica, v. 40.
2175-1188
0037-8712
10.5269/bspm.47770
2-s2.0-85124081366
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Boletim da Sociedade Paranaense de Matematica
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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_ 1808128268830769152

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