FRUSTRATION, STABILITY, AND DELAY-INDUCED OSCILLATIONS IN A NEURAL-NETWORK MODEL

The effect of time delays on the linear stability of equilibria in an artificial neural network of Hopfield type is analyzed. The possibilit y of delay-induced oscillations occurring is characterized in terms of properties of the (not necessarily symmetric) connection matrix of th e network. Such oscillations are possible exactly when the network is frustrated, equivalently when the signed digraph of the matrix does no t require the Perron property. Nonlinear analysis (centre manifold com putation) of a three-unit frustrated network is presented, giving the nature of the bifurcations taking place. A supercritical Hopf bifurcat ion is shown to occur, and a codimension-two bifurcation is unfolded.