FAIXA DINÂMICA EM REDES NEURONAIS MODELADAS POR AUTÔMATOS CELULARES

Abstract

In this thesis, we use mathematical models to study the dynamic range of neural networks. The dynamic range is the difference between maximum and minimum levels of sensation produced by known stimuli. Using cellular automata to model neuronal dynamics and different network topologies with different types of synapses, we investigate for which conditions the dynamic range is enhanced. In a network where local connections represent the electrical synapses and nonlocal connections the chemical synapses, we analyze the dynamic range in function of the number of nonlocal connections and time delay between these connections. We find that the dynamic range is enhanced for neural networks with low time delay when the number of nonlocal connections increases. Furthermore, we propose a neural network model separated into two layers, where one layer corresponds to inhibitory and the other to excitatory neurons. We randomly distribute electrical and chemical synapses in the network in order to analyse the effects on the dynamic range. In our proposed model, the chemical synapses, that are directed, can be excitatory or inhibitory, while the electrical synapses are bidirectional. Through the mean-field approximation, we analytically calculate the dynamic range as a function of the model parameters. The values that we find are very close to the results obtained from simulations. We verify that electrical synapses have a complementary effect on the enhancement of the dynamic range. Finally, we found that electrical synapses on excitatory layer are responsible for this complementary effect, while the electrical synapses in inhibitory layer promote a small increase in the dynamic range value.