We describe general characteristics of the Hodgkin-Huxley neuron's response to a periodic train of short current pulses with Gaussian noise. The deterministic neuron is bistable for antiresonant frequencies. When the stimuli arrive at the resonant frequency the firing rate is a continuous function of the current amplitude $I_0$ and scales as $(I_0-I_{th})^{1/2}$, where $I_{th}$ is an approximate threshold. Intervals of continuous irregular response alternate with integer mode-locked regions with bistable excitation edge. There is an even-all multimodal transition between the 2:1 and 3:1 states in the vicinity of the main resonance, which is analogous to the odd-all transition discovered earlier in the high-frequency regime. For $I_0<I_{th}$ and small noise the firing rate has a maximum at the resonant frequency. For larger noise and subthreshold stimulation the maximum firing rate initially shifts towards lower frequencies, then returns to higher frequencies in the limit of large noise. The stochastic coherence antiresonance, defined as the maximum of the coefficient of variation as a function of noise intensity, occurs over a wide range of parameter values, including monostable regions.
Comparisons of wave dynamics in Hodgkin-Huxley and Markov-state formalisms for the Sodium (Na) channel in some mathematical models for human cardiac tissue
Proposed tests of the soliton wave model of action potentials, and of inducible lipid pores, and how non-electrical phenomena might be consistent with the Hodgkin-Huxley model
In the last fifteen years a debate emerged about the validity of the famous Hodgkin-Huxley model for nerve impulse. Mechanical models have been proposed. This note reviews the experimental properties of the nerve impulse and discusses the proposed alternatives. The experimental data, which rule out some of the alternative suggestions, show that, while the Hodgkin-Huxley model may not be complete, it nevertheless includes essential features that should not be overlooked in the attempts made to improve, or supersede, it.
Effect of Channel Noise in Synchronization and Metabolic Energy Consumption in Unidirectionally Coupled Neurons: Drug Blocking of Sodium and Potassium Channels
Multimodal transition and stochastic antiresonance in squid giant axons
对N.高桥，Y. Hanyu，T.穆沙河Kubo和G. Matsumoto，Physica D \textbf{43}，318（1990），关于短电流脉冲的周期序列刺激的鱿鱼巨轴突的响应在Hodgkin-Huxley模型内解释。在高频状态下，作为刺激幅度$I_0$的函数的放电率的最小值是由于多模态过渡。在该奇异点以下，仅剩下驱动周期的奇数倍，并且系统对噪声高度敏感。变异系数有一个最大值，发射率有一个最小值作为噪声强度的函数，这是一个随机相干反共振的指示。模型计算再现了在过渡附近最常见模式的发生频率。同时也证实了上述跃迁的输出频率与$I_0$的线性关系。
