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报告题目:Fokker-Planck equations of neuron networks: numerical simulation and dilating the blowup solution

报告人: 周珍楠 助理教授（北京大学北京国际数学研究中心）

Abstract

In this talk, we are concerned with the Fokker-Planck equations associated with the Nonlinear Noisy Leaky Integrate-and-Fire model for neuron networks. Due to the jump mechanism at the microscopic level, such Fokker-Planck equations are endowed with an unconventional structure: transporting the boundary flux to a specific interior point. In the first part of the talk, we present a conservative and positivity preserving scheme for these Fokker-Planck equations, and we show that in the linear case, the semi-discrete scheme satisfies the discrete relative entropy estimate, which essentially matches the only known long time asymptotic solution property. We also provide extensive numerical tests to verify the scheme properties, and carry out several sets of numerical experiments, including finite-time blowup, convergence to equilibrium and capturing time-period solutions of the variant models. Secondly, we introduce a new notion of genealized solutions for this model with a dynamical time rescaling, so that the extension of solutions after blowups becomes possible. 

报告人简介: 周珍楠，北京大学北京国际数学研究中心助理教授。2014 年在美国威斯康辛大学麦迪逊分校获得博士学位，2014-2017 年在美国杜克大学担任助理研究教授，2017 年加入北京大学北京国际数学研究中心。主要研究领域为微分方程的应用分析，微分方程数值解，应用随机分析，随机模拟等，特别是关注来源于自然科学的应用数学问题。入选中组部第十四批“千人计划”青年人才项目（2018）。

报告时间：2023年12月15日（周五）下午15：00-16：00

报告地点：教二楼701

联系人：阮欣然