Tuckwell H C, Walsh J B
Biol Cybern. 1983;49(2):99-110. doi: 10.1007/BF00320390.
The linear cable equation with uniform Poisson or white noise input current is employed as a model for the voltage across the membrane of a one-dimensional nerve cylinder, which may sometimes represent the dendritic tree of a nerve cell. From the Green's function representation of the solutions, the mean, variance and covariance of the voltage are found. At large times, the voltage becomes asymptotically wide-sense stationary and we find the spectral density functions for various cable lengths and boundary conditions. For large frequencies the voltage exhibits "1/f3/2 noise". Using the Fourier series representation of the voltage we study the moments of the firing times for the diffusion model with numerical techniques, employing a simplified threshold criterion. We also simulate the solution of the stochastic cable equation by two different methods in order to estimate the moments and density of the firing time.
具有均匀泊松或白噪声输入电流的线性电缆方程被用作一维神经纤维膜上电压的模型，该神经纤维有时可代表神经细胞的树突。从解的格林函数表示中，求出了电压的均值、方差和协方差。在长时间情况下，电压渐近地成为广义平稳的，并且我们求出了各种电缆长度和边界条件下的谱密度函数。对于高频，电压呈现出“1/f3/2噪声”。利用电压的傅里叶级数表示，我们采用简化的阈值准则，用数值技术研究了扩散模型的放电时间矩。我们还通过两种不同的方法模拟了随机电缆方程的解，以估计放电时间的矩和密度。
