Abstract
A sufficient condition for the state of a recurrent neural network to stably converge to an equilibrium state is the symmetry of the weights of connections between constituent units, but it imposes a strong restriction on the capability of the network in general. Although several stability conditions have been proposed for asymmetric recurrent networks, they are too strict for checking the stability, particularly when mutual connections between units have opposite signs of weights. In this paper some new stability conditions are derived by using a novel Lyapunov function. They provide milder constraints on the connection weights than the conventional results.
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