Mathematical Neuroscience: From Neurons to Circuits to Systems
Gutkin, Pinto, Ermentrout; Journal of Physiology - Paris 97 (2003) 209–219.
Applications of mathematics and computational techniques to our understanding of neuronal systems are provided. Reduction of membrane models to simplified canonical models demonstrates how neuronal spike-time statistics follow from simple properties of neurons. Averaging over space allows one to derive a simple model for the whisker barrel circuit and use this to explain and suggest several experiments. Spatio-temporal pattern formation methods are applied to explain the patterns seen in the early stages of drug-induced visual hallucinations.
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