Center for Physical Sciences and Technology, LT-10257 Vilnius, Lithuania.
Phys Rev E. 2019 Nov;100(5-1):052211. doi: 10.1103/PhysRevE.100.052211.
We consider the effect of small independent local noise on a network of quadratic integrate-and-fire neurons, globally coupled via synaptic pulses of finite width. The Fokker-Planck equation for a network of infinite size is reduced to a low-dimensional system of ordinary differential equations using the recently proposed perturbation theory based on circular cumulants. A bifurcation analysis of the reduced equations is performed, and areas in the parameter space, where the noise causes macroscopic oscillations of the network, are determined. The validity of the reduced equations is verified by comparing their solutions with "exact" solutions of the Fokker-Planck equation, as well as with the results of direct simulation of stochastic microscopic dynamics of a finite-size network.
我们考虑了小的独立局部噪声对通过有限宽度突触脉冲全局耦合的二次积分点火神经元网络的影响。使用最近提出的基于循环累积量的微扰理论，将无限大网络的福克-普朗克方程简化为低维常微分方程组。对简化方程进行了分岔分析，确定了噪声引起网络宏观振荡的参数空间区域。通过将简化方程的解与福克-普朗克方程的“精确”解以及有限大小网络的随机微观动力学的直接模拟结果进行比较，验证了简化方程的有效性。
