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.

我们借助有向树晶格模型研究了具有多个弱延迟反馈的嘈杂可兴奋单元中的随机突发现象。我们发现出现的峰值序列和功率谱密度表达式的统计特性。这个简单的模型被扩展到具有星型延迟耦合的三个单元的网络。我们找到每个单元的功率谱密度和任意两个单元之间的交叉谱密度。分析方法背后的基本假设是时间尺度的分离，允许将脉冲序列描述为一个点过程，以及耦合的弱点，允许通过单脉冲激发的总和来表示重叠脉冲的作用概率。