Neuronal dynamics under periodic stimuli

The convergence characteristics of a single dissipative Hopfield-type neuron with self-interaction under periodic external stimuli are considered. Sufficient conditions are established for associative encoding and recall of the periodic patterns associated with the external stimuli. Both continuous-time-continuous-state and discrete-time-continuous-state models are discussed. It is shown that when the neuronal gain is dominated by the neuronal dissipation on average, associative recall of the encoded temporal pattern is guaranteed and this is achieved by the global asymptotic stability of the encoded pattern.