Existence and learning of oscillations in recurrent neural networks

In this paper we study a particular class of n-node recurrent neural networ ks (RNN's), In the 3-node case we use monotone dynamical systems theory to show, for a well-defined set of parameters, that, generically, every orbit of the RNN is asymptotic to a periodic orbit. Then we investigate whether R NN's of this class can adapt their internal parameters so as to "learn" and then replicate autonomously tin feedback) certain external periodic signal s. Our learning algorithm is similar to identification algorithms in adapti ve control theory. The main feature of the algorithm is that global exponen tial convergence of parameters is guaranteed. We also obtain partial conver gence results in the n-node case.