Li Yao, Chariker Logan, Young Lai-Sang
Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, 01002, USA.
Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012, USA.
J Math Biol. 2019 Jan;78(1-2):83-115. doi: 10.1007/s00285-018-1268-0. Epub 2018 Jul 30.
This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations. Rigorous results on existence and uniqueness of nonequilibrium steady states are proved. These network models are then compared to very simple reduced models driven by the same mean excitatory and inhibitory currents. Discrepancies in firing rates between network and reduced models are investigated and explained by correlations in spiking, or partial synchronization, working in concert with "nonlinearities" in the time evolution of membrane potentials. The use of simple random walks and their first passage times to simulate fluctuations in neuronal membrane potentials and interspike times is also considered.
本文介绍了一类相互作用神经元的随机模型，其涌现动力学类似于在局部皮层群体中观察到的动力学。证明了非平衡稳态存在性和唯一性的严格结果。然后将这些网络模型与由相同平均兴奋性和抑制性电流驱动的非常简单的简化模型进行比较。研究了网络模型和简化模型之间放电率的差异，并通过尖峰相关性或部分同步与膜电位时间演化中的“非线性”协同作用来解释。还考虑了使用简单随机游走及其首次通过时间来模拟神经元膜电位和峰间期的波动。
