相互作用的二维非线性随机脉冲神经元的平均场极限
Mean-field limit of interacting 2D nonlinear stochastic spiking neurons
摘要：
在这项工作中，我们提出了一个非线性随机模型的随机尖峰神经元网络。我们推导了该系统的平均场极限。然后，我们设计了一个蒙特卡罗方法的微观系统的模拟，和有限体积法（基于迎风隐格式计划）的平均场模型。有限体积法尊重数值版本的两个主要性质的平均场模型，守恒和积极的，导致存在性和唯一性的数值解。由于网络的大小趋于无穷大，我们数值观察到传播的混沌和收敛从一个单独的描述，平均场的描述。数值证据的存在的Hopf分岔（同步活动的同义词）的一个足够高的连接值，提供。
英文摘要：
In this work, we propose a nonlinear stochastic model of a network of stochastic spiking neurons. We heuristically derive the mean-field limit of this system. We then design a Monte Carlo method for the simulation of the microscopic system, and a finite volume method (based on an upwind implicit scheme) for the mean-field model. The finite volume method respects numerical versions of the two main properties of the mean-field model, conservation and positivity, leading to existence and uniqueness of a numerical solution. As the size of the network tends to infinity, we numerically observe propagation of chaos and convergence from an individual description to a mean-field description. Numerical evidences for the existence of a Hopf bifurcation (synonym of synchronised activity) for a sufficiently high value of connectivity, are provided.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
