Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Strasse 24/25, 14476, Potsdam-Golm, Germany.
Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, Nizhny Novgorod, Russia, 606950.
Biol Cybern. 2022 Apr;116(2):121-128. doi: 10.1007/s00422-021-00883-9. Epub 2021 Jun 28.
We investigate the phenomenon of stochastic bursting in a noisy excitable unit with multiple weak delay feedbacks, by virtue of a directed tree lattice model. We find statistical properties of the appearing sequence of spikes and expressions for the power spectral density. This simple model is extended to a network of three units with delayed coupling of a star type. We find the power spectral density of each unit and the cross-spectral density between any two units. The basic assumptions behind the analytical approach are the separation of timescales, allowing for a description of the spike train as a point process, and weakness of coupling, allowing for a representation of the action of overlapped spikes via the sum of the one-spike excitation probabilities.
我们借助有向树格模型研究了在具有多个弱延迟反馈的噪声兴奋性单元中随机突发的现象。我们发现了尖峰出现序列的统计特性和功率谱密度的表达式。此简单模型扩展到了具有星型延迟耦合的三个单元网络。我们找到了每个单元的功率谱密度和任意两个单元之间的互功率谱密度。分析方法背后的基本假设是时间尺度的分离，这允许将尖峰序列描述为一个点过程，以及耦合的弱度，这允许通过单尖峰激发概率的和来表示重叠尖峰的作用。
