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Neuronal dynamics in time varying environments: Continuous and discrete time models. (English) Zbl 1007.92008

Summary: The convergence characteristics of an isolated Hopfield-type neuron in time varying environments are considered in particular when the neuronal parameters are assumed to be almost periodic. This study includes the investigations of neurons having periodic parameters but the periods are not integrally dependent. Both continuous-time-continuous-state and discrete-time-continuous-state models are discussed. Sufficient conditions are established for associative encoding and recall of the temporally non-uniform pattern associated with the external stimulus. 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 stability of the encoded pattern.

MSC:

92C20 Neural biology
34C60 Qualitative investigation and simulation of ordinary differential equation models
37N25 Dynamical systems in biology
39A12 Discrete version of topics in analysis
65C20 Probabilistic models, generic numerical methods in probability and statistics
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