D'Onofrio Giuseppe, Tamborrino Massimiliano, Lansky Petr
Institute of Physiology of the Czech Academy of Sciences, Videnska 1083, 14220 Prague 4, Czech Republic.
Johannes Kepler University Linz, Institute for Stochastics Altenbergerstraße 69, 4040 Linz, Austria.
Chaos. 2018 Oct;28(10):103119. doi: 10.1063/1.5051494.
The Jacobi process is a stochastic diffusion characterized by a linear drift and a special form of multiplicative noise which keeps the process confined between two boundaries. One example of such a process can be obtained as the diffusion limit of the Stein's model of membrane depolarization which includes both excitatory and inhibitory reversal potentials. The reversal potentials create the two boundaries between which the process is confined. Solving the first-passage-time problem for the Jacobi process, we found closed-form expressions for mean, variance, and third moment that are easy to implement numerically. The first two moments are used here to determine the role played by the parameters of the neuronal model; namely, the effect of multiplicative noise on the output of the Jacobi neuronal model with input-dependent parameters is examined in detail and compared with the properties of the generic Jacobi diffusion. It appears that the dependence of the model parameters on the rate of inhibition turns out to be of primary importance to observe a change in the slope of the response curves. This dependence also affects the variability of the output as reflected by the coefficient of variation. It often takes values larger than one, and it is not always a monotonic function in dependency on the rate of excitation.
雅可比过程是一种随机扩散过程，其特征在于线性漂移和一种特殊形式的乘性噪声，这种噪声使该过程限制在两个边界之间。这种过程的一个例子可以通过斯坦因膜去极化模型的扩散极限得到，该模型包括兴奋性和抑制性反转电位。反转电位形成了该过程所限制的两个边界。通过求解雅可比过程的首次通过时间问题，我们得到了均值、方差和三阶矩的闭式表达式，这些表达式易于进行数值实现。这里使用前两个矩来确定神经元模型参数所起的作用；具体而言，详细研究了乘性噪声对具有输入依赖参数的雅可比神经元模型输出的影响，并将其与一般雅可比扩散的性质进行了比较。结果表明，模型参数对抑制率的依赖性对于观察响应曲线斜率的变化至关重要。这种依赖性还会影响输出的变异性，如变异系数所反映的那样。它通常取值大于1，并且并不总是关于激发率的单调函数。
