On the stability, storage capacity, and design of nonlinear continuous neural networks

The stability, capacity, and design of a nonlinear continuous neural network are analyzed. Sufficient conditions for existence and asymptotic stability of the network's equilibria are reduced to a set of piecewise-linear inequality relations that can be solved by a feedforward binary network, or by methods such as Fourier elimination. The stability and capacity of the network is characterized by the postsynaptic firing rate function. An N-neuron network with sigmoidal firing function is shown to have up to 3/sup N/ equilibrium points. This offers a higher capacity than the (0.1-0.2)N obtained in the binary Hopfield network. It is shown that by a proper selection of the postsynaptic firing rate function, one can significantly extend the capacity storage of the network.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>