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Asymptotic Behavior and Synchronizability Characteristics of a Class of Recurrent Neural Networks

cebulla{at}wiener.iam.uni-bonn.de Institute for Applied Mathematics, Universität Bonn, D-53115 Bonn, Germany

We propose an approach to the analysis of the influence of the topology of a neural network on its synchronizability in the sense of equal output activity rates given by a particular neural network model. The model we introduce is a variation of the Zhang model. We investigate the time-asymptotic behavior of the corresponding dynamical system (in particular, the conditions for the existence of an invariant compact asymptotic set) and apply the results of the synchronizability analysis on a class of random scale free networks and to the classical random networks with Poisson connectivity distribution.