Dynamic recurrent neural networks: a dynamical analysis

Abstract
In this paper, we explore the dynamical features of a neural network model which presents two types of adaptative parameters: the classical weights between the units and the time constants associated with each artificial neuron. The purpose of this study is to provide a strong theoretical basis for modeling and simulating dynamic recurrent neural networks. In order to achieve this, we study the effect of the statistical distribution of the weights and of the time constants on the network dynamics and we make a statistical analysis of the neural transformation. We examine the network power spectra (to draw some conclusions over the frequential behaviour of the network) and we compute the stability regions to explore the stability of the model. We show that the network is sensitive to the variations of the mean values of the weights and the time constants (because of the temporal aspects of the learned tasks). Nevertheless, our results highlight the improvements in the network dynamics due to the introduction of adaptative time constants and indicate that dynamic recurrent neural networks can bring new powerful features in the field of neural computing.