Bifurcation Structure of an Electronic Circuit Model for Neuronal Firings

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  • 神経興奮の電子回路モデルが示す分岐構造
  • シンケイ コウフン ノ デンシ カイロ モデル ガ シメス ブンキ コウゾウ

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Abstract

Neuron dynamics, shown by an excitable membrane, were replicated using a two-terminal electronic circuit (Murai et al. 1977; Hoshimiya et al. 1979), which was composed of four diffierent kinds of current: corresponding to capacitance, leakage, sodium and potassium currents. The main purpose of this paper is to clarify that the electronic circuit is equivalent to the Hodgkin-Huxley equations, from a topological point of view. To this end, we introduce continuous differential equations reproducing bifurcation structures shown quantitatively by the electronic circuit. In the electronic circuit, the parameter EK, the potassium equilibrium potentail proposed by authors, is responsible for reproducing bifurcation structures of the Hodgkin-Huxley equation.

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