Aihara K, Matsumoto G, Ikegaya Y
J Theor Biol. 1984 Jul 21;109(2):249-69. doi: 10.1016/s0022-5193(84)80005-3.
Membrane potential responses of a Hodgkin-Huxley oscillator to an externally-applied sinusoidal current were numerically calculated with relation to bifurcation parameters of the amplitude and the frequency of the stimulating current. The Hodgkin-Huxley oscillator, or the Hodgkin-Huxley axon in the state of self-sustained oscillation of action potentials, was realized by immersing the axon in calcium-deficient sea water. The forced oscillations were analysed by the stroboscopic plots and/or the Lorenz plots. The results show that the periodically forced Hodgkin-Huxley oscillator exhibits not only periodic motions (harmonic or sub-harmonic synchronization) but also non-periodic motions (quasi-periodic or chaotic oscillation), that the motions were determined by the amplitude and the frequency of the stimulating current, and that the characteristic motions obtained in the present study were in reasonable agreement with those of our previous results, found experimentally in squid giant axons. Also, two kinds of routes to the chaotic oscillations were found; successive period-doubling bifurcations and formation of the intermittently chaotic oscillation from sub-harmonic synchronization.
针对霍奇金-赫胥黎振荡器对外部施加的正弦电流的膜电位响应，结合刺激电流的幅度和频率的分岔参数进行了数值计算。霍奇金-赫胥黎振荡器，即处于动作电位自持振荡状态的霍奇金-赫胥黎轴突，是通过将轴突浸入缺钙海水中实现的。通过频闪图和/或洛伦兹图对受迫振荡进行了分析。结果表明，周期性受迫的霍奇金-赫胥黎振荡器不仅表现出周期性运动（谐波或次谐波同步），还表现出非周期性运动（准周期性或混沌振荡），这些运动由刺激电流的幅度和频率决定，并且本研究中获得的特征运动与我们之前在鱿鱼巨轴突中通过实验发现的结果合理一致。此外，还发现了通往混沌振荡的两种途径；连续的倍周期分岔以及从次谐波同步形成间歇性混沌振荡。
