A Simple Chaotic Neuron Model : Stochastic Behavior of Neural Networks

TL;DR

This paper introduces a simple stochastic neuron model that exhibits chaotic behavior, producing EEG-like signals and offering insights into neural system dynamics through Monte Carlo simulations.

Contribution

The paper presents a novel stochastic neuron model using Monte Carlo methods that demonstrates chaotic EEG-like signals, advancing understanding of neural dynamics.

Findings

EEG-like signals with phase portraits generated

Lyapunov exponent indicates chaos

Correlation dimension found to be 0.92

Abstract

We have shortly reviewed the occurrence of the post-synaptic potentials between neurons, the relation between EEG and neuron dynamics, as well as methods of signal analysis. We supposed a simple stochastic model representing electrical activity of neuronal systems. The model is constructed using the Monte Carlo simulation technique. The results yielded EEG-like signals with their phase portraits in three-dimensional space. The Lyapunov exponent was positive, indicating a chaotic behavior. The correlation dimension of the EEG-like signals was found to be .92, which was smaller than those reported by others. It was concluded that this neuron model may provide valuable clues about the dynamic behavior of neural systems.