Neuronal dynamics in time varying environments: Continuous and discrete time models

The convergence characteristics of an isolated Hopfield-type neuron in time varying environments are considered in particular when the neuronal parame ters are assumed to be almost periodic. This study includes the investigati ons of neurons having periodic parameters but the periods are not integrall y dependent. Both continuous-time-continuous-state and discrete-time-contin uous-state models are discussed. Sufficient conditions are established for associative encoding and recall of the temporally non-uniform pattern assoc iated with the external stimulus. It is shown that when the neuronal gain i s dominated by the neuronal dissipation on average, associative recall of t he encoded temporal pattern is guaranteed and this is achieved by the globa l stability of the encoded pattern.