A numerical solver for a nonlinear Fokker-Planck equation representation   of neuronal network dynamics

doi:10.1016/j.jcp.2010.10.027

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	A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics
	Caceres, Maria J. ; Carrillo, Jose A. ; Tao, Louis
刊名	计算物理学杂志
	2011
关键词	Neuronal network Kinetic equations Fokker-Planck equation Direct simulation Monte Carlo Deterministic simulations WENO methods Chang-Cooper method POPULATION-DENSITY APPROACH PRIMARY VISUAL-CORTEX REALISTIC SYNAPTIC KINETICS BOLTZMANN-POISSON SYSTEM MONTE-CARLO METHODS NEURAL-NETWORKS EFFICIENT IMPLEMENTATION ORIENTATION SELECTIVITY SEMICONDUCTOR-DEVICES ASYNCHRONOUS STATES
DOI	10.1016/j.jcp.2010.10.027
英文摘要	To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [15,14], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [15] to further simplify the kinetic theory. (C) 2010 Elsevier Inc. All rights reserved.; Computer Science, Interdisciplinary Applications; Physics, Mathematical; SCI(E); 9; ARTICLE; 4; 1084-1099; 230
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/241395]
专题	生命科学学院
推荐引用方式 GB/T 7714	Caceres, Maria J.,Carrillo, Jose A.,Tao, Louis. A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics[J]. 计算物理学杂志,2011.
APA	Caceres, Maria J.,Carrillo, Jose A.,&Tao, Louis.(2011).A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics.计算物理学杂志.
MLA	Caceres, Maria J.,et al."A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics".计算物理学杂志 (2011).