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

NATALI GUISANDE; MONSERRAT PALLARES DI NUNZIO; NATANIEL MARTINEZ; OSVALDO ANIBAL ROSSO; FERNANDO MONTANI

Chaos

American Institute of Physics Inc.

Lugar: New York; Año: 2023 vol. 33 p. 43111 - 43120

In this study, the Hénon map was analyzed using quantifiers from information theory in order to compare its dynamics to experimentaldata from brain regions known to exhibit chaotic behavior. The goal was to investigate the potential of the Hénon map as a model forreplicating chaotic brain dynamics in the treatment of Parkinson’s and epilepsy patients. The dynamic properties of the Hénon map werecompared with data from the subthalamic nucleus, the medial frontal cortex, and a q-DG model of neuronal input–output with easy numericalimplementation to simulate the local behavior of a population. Using information theory tools, Shannon entropy, statistical complexity, andFisher’s information were analyzed, taking into account the causality of the time series. For this purpose, different windows over the timeseries were considered. The findings revealed that neither the Hénon map nor the q-DG model could perfectly replicate the dynamics ofthe brain regions studied. However, with careful consideration of the parameters, scales, and sampling used, they were able to model somecharacteristics of neural activity. According to these results, normal neural dynamics in the subthalamic nucleus region may present a morecomplex spectrum within the complexity–entropy causality plane that cannot be represented by chaotic models alone. The dynamic behaviorobserved in these systems using these tools is highly dependent on the studied temporal scale. As the size of the sample studied increases, thedynamics of the Hénon map become increasingly different from those of biological and artificial neural systems.