Chaotic Dynamical Behavior of Recurrent Neural Network

On account of their role played in the fundamental biological rhythms and by considering their potential use in information processing, the dynamical properties of an artificial neural network are particularly interesting to investigate. In order to reduce the degree of complexity of this work, we have considered in this paper a fully connected neural network of two discrete neurons. We have proceeded to a qualitative and quantitative study of their state evolution by means of numerical simulation. The first aim was to find the possible equilibrium states. Other authors have already shown that some oscillating state can occur. So, the second aim was to analyze the dynamical properties of each of them. We have computed the value of the Lyapunov’s exponents and the fractal dimension. The sensitivity of the dynamical characteristics to parameters such as the weights of the connections and the shape of the activation function has been studied.

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