Chaotic dynamics of the Hénon map and neuronal input–output: A comparison with neurophysiological data

Autores
Guisande, Natalí; Pallares Di Nunzio, Monserrat; Martinez, Nataniel; Rosso, Osvaldo Aníbal; Montani, Fernando Fabián
Año de publicación
2023
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this study, the Hénon map was analyzed using quantifiers from information theory in order to compare its dynamics to experimental data from brain regions known to exhibit chaotic behavior. The goal was to investigate the potential of the Hénon map as a model for replicating chaotic brain dynamics in the treatment of Parkinson’s and epilepsy patients. The dynamic properties of the Hénon map were compared with data from the subthalamic nucleus, the medial frontal cortex, and a q-DG model of neuronal input–output with easy numerical implementation to simulate the local behavior of a population. Using information theory tools, Shannon entropy, statistical complexity, and Fisher’s information were analyzed, taking into account the causality of the time series. For this purpose, different windows over the time series were considered. The findings revealed that neither the Hénon map nor the q-DG model could perfectly replicate the dynamics of the brain regions studied. However, with careful consideration of the parameters, scales, and sampling used, they were able to model some characteristics of neural activity. According to these results, normal neural dynamics in the subthalamic nucleus region may present a more complex spectrum within the complexity–entropy causality plane that cannot be represented by chaotic models alone. The dynamic behavior observed in these systems using these tools is highly dependent on the studied temporal scale. As the size of the sample studied increases, the dynamics of the Hénon map become increasingly different from those of biological and artificial neural systems.
Instituto de Física La Plata
Materia
Física
Hénon map
q-DG model of neuronal input–output
Shannon entropy
dynamic behavior
neurophysiological signals
complex spectrumof dynamical characteristics
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/160848

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repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Chaotic dynamics of the Hénon map and neuronal input–output: A comparison with neurophysiological dataGuisande, NatalíPallares Di Nunzio, MonserratMartinez, NatanielRosso, Osvaldo AníbalMontani, Fernando FabiánFísicaHénon mapq-DG model of neuronal input–outputShannon entropydynamic behaviorneurophysiological signalscomplex spectrumof dynamical characteristicsIn this study, the Hénon map was analyzed using quantifiers from information theory in order to compare its dynamics to experimental data from brain regions known to exhibit chaotic behavior. The goal was to investigate the potential of the Hénon map as a model for replicating chaotic brain dynamics in the treatment of Parkinson’s and epilepsy patients. The dynamic properties of the Hénon map were compared with data from the subthalamic nucleus, the medial frontal cortex, and a q-DG model of neuronal input–output with easy numerical implementation to simulate the local behavior of a population. Using information theory tools, Shannon entropy, statistical complexity, and Fisher’s information were analyzed, taking into account the causality of the time series. For this purpose, different windows over the time series were considered. The findings revealed that neither the Hénon map nor the q-DG model could perfectly replicate the dynamics of the brain regions studied. However, with careful consideration of the parameters, scales, and sampling used, they were able to model some characteristics of neural activity. According to these results, normal neural dynamics in the subthalamic nucleus region may present a more complex spectrum within the complexity–entropy causality plane that cannot be represented by chaotic models alone. The dynamic behavior observed in these systems using these tools is highly dependent on the studied temporal scale. As the size of the sample studied increases, the dynamics of the Hénon map become increasingly different from those of biological and artificial neural systems.Instituto de Física La Plata2023-04-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/160848enginfo:eu-repo/semantics/altIdentifier/issn/1089-7682info:eu-repo/semantics/altIdentifier/doi/10.1063/5.0142773info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:42:01Zoai:sedici.unlp.edu.ar:10915/160848Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:42:01.654SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Chaotic dynamics of the Hénon map and neuronal input–output: A comparison with neurophysiological data
title Chaotic dynamics of the Hénon map and neuronal input–output: A comparison with neurophysiological data
spellingShingle Chaotic dynamics of the Hénon map and neuronal input–output: A comparison with neurophysiological data
Guisande, Natalí
Física
Hénon map
q-DG model of neuronal input–output
Shannon entropy
dynamic behavior
neurophysiological signals
complex spectrumof dynamical characteristics
title_short Chaotic dynamics of the Hénon map and neuronal input–output: A comparison with neurophysiological data
title_full Chaotic dynamics of the Hénon map and neuronal input–output: A comparison with neurophysiological data
title_fullStr Chaotic dynamics of the Hénon map and neuronal input–output: A comparison with neurophysiological data
title_full_unstemmed Chaotic dynamics of the Hénon map and neuronal input–output: A comparison with neurophysiological data
title_sort Chaotic dynamics of the Hénon map and neuronal input–output: A comparison with neurophysiological data
dc.creator.none.fl_str_mv Guisande, Natalí
Pallares Di Nunzio, Monserrat
Martinez, Nataniel
Rosso, Osvaldo Aníbal
Montani, Fernando Fabián
author Guisande, Natalí
author_facet Guisande, Natalí
Pallares Di Nunzio, Monserrat
Martinez, Nataniel
Rosso, Osvaldo Aníbal
Montani, Fernando Fabián
author_role author
author2 Pallares Di Nunzio, Monserrat
Martinez, Nataniel
Rosso, Osvaldo Aníbal
Montani, Fernando Fabián
author2_role author
author
author
author
dc.subject.none.fl_str_mv Física
Hénon map
q-DG model of neuronal input–output
Shannon entropy
dynamic behavior
neurophysiological signals
complex spectrumof dynamical characteristics
topic Física
Hénon map
q-DG model of neuronal input–output
Shannon entropy
dynamic behavior
neurophysiological signals
complex spectrumof dynamical characteristics
dc.description.none.fl_txt_mv In this study, the Hénon map was analyzed using quantifiers from information theory in order to compare its dynamics to experimental data from brain regions known to exhibit chaotic behavior. The goal was to investigate the potential of the Hénon map as a model for replicating chaotic brain dynamics in the treatment of Parkinson’s and epilepsy patients. The dynamic properties of the Hénon map were compared with data from the subthalamic nucleus, the medial frontal cortex, and a q-DG model of neuronal input–output with easy numerical implementation to simulate the local behavior of a population. Using information theory tools, Shannon entropy, statistical complexity, and Fisher’s information were analyzed, taking into account the causality of the time series. For this purpose, different windows over the time series were considered. The findings revealed that neither the Hénon map nor the q-DG model could perfectly replicate the dynamics of the brain regions studied. However, with careful consideration of the parameters, scales, and sampling used, they were able to model some characteristics of neural activity. According to these results, normal neural dynamics in the subthalamic nucleus region may present a more complex spectrum within the complexity–entropy causality plane that cannot be represented by chaotic models alone. The dynamic behavior observed in these systems using these tools is highly dependent on the studied temporal scale. As the size of the sample studied increases, the dynamics of the Hénon map become increasingly different from those of biological and artificial neural systems.
Instituto de Física La Plata
description In this study, the Hénon map was analyzed using quantifiers from information theory in order to compare its dynamics to experimental data from brain regions known to exhibit chaotic behavior. The goal was to investigate the potential of the Hénon map as a model for replicating chaotic brain dynamics in the treatment of Parkinson’s and epilepsy patients. The dynamic properties of the Hénon map were compared with data from the subthalamic nucleus, the medial frontal cortex, and a q-DG model of neuronal input–output with easy numerical implementation to simulate the local behavior of a population. Using information theory tools, Shannon entropy, statistical complexity, and Fisher’s information were analyzed, taking into account the causality of the time series. For this purpose, different windows over the time series were considered. The findings revealed that neither the Hénon map nor the q-DG model could perfectly replicate the dynamics of the brain regions studied. However, with careful consideration of the parameters, scales, and sampling used, they were able to model some characteristics of neural activity. According to these results, normal neural dynamics in the subthalamic nucleus region may present a more complex spectrum within the complexity–entropy causality plane that cannot be represented by chaotic models alone. The dynamic behavior observed in these systems using these tools is highly dependent on the studied temporal scale. As the size of the sample studied increases, the dynamics of the Hénon map become increasingly different from those of biological and artificial neural systems.
publishDate 2023
dc.date.none.fl_str_mv 2023-04-03
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/160848
url http://sedici.unlp.edu.ar/handle/10915/160848
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/1089-7682
info:eu-repo/semantics/altIdentifier/doi/10.1063/5.0142773
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
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repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
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