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

Abstract

In this study, the H´enon 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 H´enon map as a model for replicating chaotic brain dynamics in the treatment of Parkinson´s and epilepsy patients. The dynamic properties of the H´enon map were compared with data from the subthalamic nucleus, the medial frontal cortex, and a mbox{$q$-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 H´enon map nor the mbox{$q$-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 H´enon map become increasingly different from those of biological and artificial neural systems.