Hodgkin-Huxley方程式の大域的分岐構造とパラメータ依存度

概要

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The Hodgkin-Huxley (HH) equations of a squid giant axon are the most important mathematical model in electrophysiology and biology, and are also important in the development of various biologically inspired intelligent devices such as artificial neuron device and neural networks. The HH equations, however, include various constants or parameters whose values were determined based on physiological experiments, and thus the values possess inherent ambiguities. Also, the ‘constants’ are not really constant but change temporally. Thus, in this paper, we study the effects of the change of the constants or parameters on the dynamics of the HH equations and consider the parameter dependence and sensitivity of the equations; we study the bifurcation structure of the HH equations by changing their various parameters. In particular, we take the voltage-dependency of the dynamics of so-called gating variables as typical bifurcation parameters and show that the HH dynamics is very sensitive to the steady-state functions but not sensitive to the time ‘constants’ of gating variables.
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