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Abstract

The method of averaging and a detailed bifurcation calculationare used to reduce a system of synaptically coupled neurons to aHopfield type continuous time neural network. Due to some specialproperties of the bifurcation, explicit averaging is not requiredand the reduction becomes a simple algebraic problem. The resultantcalculations show one how to derive a new type of "squashingfunction" whose properties are directly related to the detailedionic mechanisms of the membrane. Frequency encoding as opposed toamplitude encoding emerges in a natural fashion from the theory.The full system and the reduced system are numericallycompared.