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.
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April 2023
Research Article|
April 03 2023
Chaotic dynamics of the Hénon map and neuronal input–output: A comparison with neurophysiological data
Special Collection:
Ordinal Methods: Concepts, Applications, New Developments and Challenges
Natalí Guisande
;
Natalí Guisande
(Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review & editing)
1
Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata
, Diagonal 113 entre 63 y 64, La Plata 1900, Buenos Aires, Argentina
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Monserrat Pallares di Nunzio
;
Monserrat Pallares di Nunzio
(Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Validation)
1
Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata
, Diagonal 113 entre 63 y 64, La Plata 1900, Buenos Aires, Argentina
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Nataniel Martinez
;
Nataniel Martinez
(Conceptualization, Data curation, Investigation)
2
Instituto de Física de Mar del Plata, Universidad Nacional de Mar del Plata & CONICET
, Mar del Plata 7600, Buenos Aires, Argentina
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Osvaldo A. Rosso
;
Osvaldo A. Rosso
(Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing)
1
Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata
, Diagonal 113 entre 63 y 64, La Plata 1900, Buenos Aires, Argentina
3
Instituto de Física, Universidade Federal de Alagoas (UFAL)
, BR 104 Norte km 97, 57072-970 Maceió, Brazil
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Fernando Montani
Fernando Montani
a)
(Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing)
1
Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata
, Diagonal 113 entre 63 y 64, La Plata 1900, Buenos Aires, Argentina
a)Author to whom correspondence should be addressed: f.montani@fisica.unlp.edu.ar
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a)Author to whom correspondence should be addressed: f.montani@fisica.unlp.edu.ar
Note: This paper is part of the Focus Issue on Ordinal Methods: Concepts, Applications, New Developments and Challenges.
Chaos 33, 043111 (2023)
Article history
Received:
January 17 2023
Accepted:
March 10 2023
Citation
Natalí Guisande, Monserrat Pallares di Nunzio, Nataniel Martinez, Osvaldo A. Rosso, Fernando Montani; Chaotic dynamics of the Hénon map and neuronal input–output: A comparison with neurophysiological data. Chaos 1 April 2023; 33 (4): 043111. https://doi.org/10.1063/5.0142773
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