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Stability in a model of a delayed neural network
Authors:Jacques Bélair
Institution:(1) Département de mathématiques et statistique and Centre de recherches mathématiques, Université de Montréal, C.P. 6128-A, H3C 3J7 Montréal, Québec, Canada;(2) Centre for Nonlinear Dynamics in Physiology and Medicine, McGill University, Montréal, Québec, Canada
Abstract:The stability of the null solution in a system of coupled cells is investigated. Each cell evolves according to Hopfield's equation for an analog circuit, with a delay incorporated to account for finite switching speed of amplifiers. A necessary and sufficient condition on the connection matrix is obtained for delay-induced oscillations to be possible in a general (not necessarily symmetric) network.
Keywords:Neural networks  time delays  oscillations
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