Stochastic neural field model: multiple firing events and correlations
Stochastic neural field model: multiple firing events and correlations
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DOI：
10.1007/s00285-019-01389-6
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发表时间：
2019-07
影响因子：
1.9
通讯作者：
Yao Li;Hui Xu
中科院分区：
文献类型：
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作者：
Yao Li;Hui Xu
本文研究了空间异质随机神经场模型中的一种称为多重发射事件（multiple firing event， MFE）的非线性动力学现象，该模型是在我们之前的论文（Li et al. in J Math Biol 78:83-115, 2018）的基础上进行扩展的。mfe是部分同步的尖峰阵，被认为是伽马振荡的原因。证明了关于随机稳定性和大数定律的严密结果，进一步表明了与MFEs相关的许多量的良好定义性和可计算性。在此基础上，我们进一步研究了mfe的时空特性。我们的主要发现是mfe具有空间相关性，但空间相关性衰减很快。在定性模型的基础上进行了详细的数学论证，旨在论证mfe的机制。
This paper studies a nonlinear dynamical phenomenon called the multiple firing event (MFE) in a spatially heterogeneous stochastic neural field model, which is extended from that in our previous paper (Li et al. in J Math Biol 78:83–115, 2018). MFEs are a partially synchronized spiking barrages that are believed to be responsible for the Gamma oscillation. Rigorous results about the stochastic stability and the law of large numbers are proved, which further imply the well-definedness and computability of many quantities related to MFEs. Then we devote to study spatial and temporal properties of MFEs. Our key finding is that MFEs are spatially correlated but the spatial correlation decays quickly. Detailed mathematical justifications are made based on our qualitative models that aim to demonstrate the mechanism of MFEs.