Shimokawa T, Pakdaman K, Takahata T, Tanabe S, Sato S
Graduate School of Engineering Science, Osaka University, Toyonaka, Japan.
Biol Cybern. 2000 Oct;83(4):327-40. doi: 10.1007/s004220000156.
We present a general method for the analysis of the discharge trains of periodically forced noisy leaky integrate-and-fire neuron models. This approach relies on the iterations of a stochastic phase transition operator that generalizes the phase transition function used for the study of periodically forced deterministic oscillators to noisy systems. The kernel of this operator is defined in terms of the the first passage time probability density function of the Ornstein Uhlenbeck process through a suitable threshold. Numerically, it is computed as the solution of a singular integral equation. It is shown that, for the noisy system, quantities such as the phase distribution (cycle histogram), the interspike interval distribution, the autocorrelation function of the intervals, the autocorrelogram and the power spectrum density of the spike train, as well as the input-output cross-correlation and cross-spectral density can all be computed using the stochastic phase transition operator. A detailed description of the numerical implementation of the method, together with examples, is provided.
我们提出了一种用于分析周期性强迫噪声泄漏积分发放神经元模型放电序列的通用方法。这种方法依赖于一个随机相变算子的迭代，该算子将用于研究周期性强迫确定性振荡器的相变函数推广到噪声系统。该算子的核是根据奥恩斯坦 - 乌伦贝克过程通过合适阈值的首次通过时间概率密度函数来定义的。在数值上，它被计算为一个奇异积分方程的解。结果表明，对于噪声系统，诸如相位分布（周期直方图）、峰间间隔分布、间隔的自相关函数、自相关图和放电序列的功率谱密度，以及输入 - 输出互相关和互谱密度等量，都可以使用随机相变算子来计算。本文还提供了该方法数值实现的详细描述以及示例。
