Noise, multistability, and delayed recurrent loops

The multistability that arises in delayed feedback control mechanisms has applications for dynamic short term memory storage. Here we investigate the effects of multiplicative, Gaussian-distributed white noise on an integrate-and-fire model of a recurrent inhibitory neural loop: when the neuron fires an inhibitory pulse decreases the membrane potential by an amount \ensuremath{\Delta} at time \ensuremath{\tau} later. For appropriate choices of \ensuremath{\tau} and \ensuremath{\Delta}, multistability occurs in the form of qualitatively different neuron firing patterns. In the absence of noise, the number and nature of the coexistent attractors can be precisely determined. When noise is added to \ensuremath{\Delta}, noise-induced transitions occur between the attractors. The mechanism for these transitions is characterized and it is shown that the rate of transitions has a nonexponential dependence on the noise variance. An electronic circuit is constructed to assess the impact of noise on memory storage.