On the single neuron model that should be used in networks modelling
A. N. Pokrovsky · 2002
In recent years various models of a single neuron were used in networks modelling. The most realistic models are developments and modifications of the classical Hodgkin-Huxley model. Neural networks using realistic models are too complex for analytical research and inconvenient for numerical methods. This is the reason why most of the authors use in networks modelling simplified models of neurons with decreasing or constant threshold. These simple models are not rigorously derived from realistic models. Therefore, one can not calculate the parameters of a simple model in accordance with characteristics of ionic channels and estimate errors of the simple model. In this paper the correct method of simplification of a realistic model by asymptotic reduction of the differential equations of the model is proposed, Asymptotic reduction is used, which not only decreases the order of differential equations of the model, but also is more convenient for numerical methods.