神経振動子の大域結合系における遅い同期振動について

摘要

A population of neuronal oscillators globally coupled through a common buffer (a mean field) was analyzed using the Hodgkin-Huxley (HH) equations, which are famous as a single neuron model. In the system, it was observed that they oscillate in a phase-locked state very slowly compared with the inherent periods of each uncoupled neuronal oscillator or their firing are inhibited completely. However, the generation mechanism of these phenomena is not clear. In this study, a population of globally coupled neuronal oscillators is analyzed using the three dimensional Bonhoeffer-van der Pol equations, which are the simpler single neuron model than the HH equations. Similarly to the case of the HH equations, there are interesting phenomena such as very slow phase-locked oscillation (compared with the inherent periods of each uncoupled neuron oscillator) or the death of all oscillations. In particular, it may sound strange, but this slow phase-locked oscillation is caused by the existence of fast oscillators. We also analyze what interactions between neuronal oscillators generate this macroscopic biological rhythm.%Hodgkin-Huxley（HH）方程式は，神経細胞の活動電位発生ダイナミクスを表現する代表的な数理モデルである．HH方程式を用いて，神経振動子の大域結合系が解析され，単一神経振動子の固有周期に比して非常に遅い同期振動や振動停止などの現象が示された．しかし，このような現象の発生機構はまだ明らかになっていない．本研究では，単一神経細胞モデルとして3次元の拡張Bonhoeffer-Van der Pol方程式を用いて，大域結合した神経振動子集団の解析を行う．（単一神経振動子の固有周期に比して）非常に遅い同期振動や振動停止などの興味深い現象が見られること，特に，速い振動子が遅い同期振動に寄与するという，一見矛盾した現象を示す．また，これらの現象の発生機構や生物リズム調節機構について議論する．