Multistability and Delayed Recurrent Loops

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Abstract
Multistable dynamical systems have important applications as pattern recognition and memory storage devices. Conditions under which time-delayed recurrent loops of spiking neurons exhibit multistability are presented. Our results are illustrated on both a simple integrate-and-fire neuron and a Hodgkin-Huxley-type neuron, whose recurrent inputs are delayed versions of their output spike trains. Two kinds of multistability with respect to initial spiking functions are found, depending on whether the neuron is excitable or repetitively firing in the absence of feedback.