Análise da faixa dinâmica em redes neuronais através de autômatos celulares

Abstract

In this work, we investigate the dynamical behavior of the neural networks utilizing a Cellular Automata approach. We consider a model with only excitatory connections and other with excitatory and inhibitory connections. In the first model, we consider chemical excitatory (with and without delay), electrical, and synapses induced by external stimulus. This model shows us that the chemical synapses are crucial to the maintenance of self-sustaining dynamics. When incorporating a high delay value or high mean perturbation rate value, the behavior of the network becomes irregular. In the second model, we consider chemical excitatory and inhibitory synapses. We consider a mean field map approximation for this model, which gives us an analytical expression for the average firing rate. This expression have a critical point, which divides the network into ceasing or ceaseless dynamics. Values lower and higher than critical point makes the network goes from ceasing activity (subcritical) to ceaseless activity (supercritical). In the critical point, the dynamical can cease or be ceaseless. For this expression, we obtain a function for the dynamical range. Results from the simulation and the analytical expression for the dynamical range are in perfect agreement and show that the amplification of the dynamical range occurs in the critical point.