Synchronous neural networks of nonlinear threshold elements with hysteresis

We use Hoffmann's suggestion [Hoffmann, G. W. (1986) J. Theor. Biol. 122, 33-67] of hysteresis in a single neuron level and determine its consequences in a synchronous network made of such neurons. We show that the overall retrieval ability in the presence of noise and the memory capacity of the network in the present model are better than in conventional models without such hysteresis. Second-order interaction further improves the retrieval ability of the network and causes hysteresis in the retrieval-noise curve for any arbitrary width of the bistable region. The convergence rate is increased by the hysteresis at high noise levels but is reduced by the hysteresis at low noise levels. Explicit formulae are given for calculations of average final convergence and noise threshold as functions of the width of the bistable region. There is neurophysiological evidence for hysteresis in single neurons, and we propose optical implementations of the present model by using ZnSe interference filters to test the predictions of the theory.