288 pp. per issue
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Neural Computation

July 1994, Vol. 6, No. 4, Pages 679-695
(doi: 10.1162/neco.1994.6.4.679)
© 1994 Massachusetts Institute of Technology
Reduction of Conductance-Based Models with Slow Synapses to Neural Nets
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The method of averaging and a detailed bifurcation calculation are used to reduce a system of synaptically coupled neurons to a Hopfield type continuous time neural network. Due to some special properties of the bifurcation, explicit averaging is not required and the reduction becomes a simple algebraic problem. The resultant calculations show one how to derive a new type of “squashing function” whose properties are directly related to the detailed ionic mechanisms of the membrane. Frequency encoding as opposed to amplitude encoding emerges in a natural fashion from the theory. The full system and the reduced system are numerically compared.