Neuronal population dynamic model: An analytic approach  

作　　者：Wentao Huang Licheng Jiao Yuelei Xu Shiping Ma Jianhua Jia 

机构地区：[1]Institute of Intelligent Information Processing, Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University, P.O. Box 224, Xi'an 710071, China [2]Department of Avionics Engineering, Engineering College of Air Force Engineering University, Xf an 710038, China

出　　处：《Progress in Natural Science:Materials International》2009年第9期1159-1163,共5页自然科学进展·国际材料（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos. 60703107 and 60703108);the National High Technology Research and Development Program of China (Grant No.2006AA01Z107);the National Basic Research Program of China (Grant No. 2006CB705700);the Program for Cheung Kong Scholars and Innovative Research Teamin University (PCSIRT, IRT0645)

摘　　要：A novel analytic approach is presented to study the population of excitatory and inhibitory spiking neurons in this paper. The evolution in time of the population dynamic equation is determined by a partial differential equation. A new function is proposed to characterize the population of excitatory and inhibitory spiking neurons, which is different from the population density function discussed by most researchers. And a novel evolution equation, which is a nonhomogeneous parabolic type equation, is derived. From this, the stationary solution and the firing rate of the stationary states are given. Last, by the Fourier transform, the time dependent solution is also obtained. This method can be used to analyze the various dynamic behaviors of neuronal populations.A novel analytic approach is presented to study the population of excitatory and inhibitory spiking neurons in this paper. The evolution in time of the population dynamic equation is determined by a partial differential equation. A new function is proposed to characterize the population of excitatory and inhibitory spiking neurons, which is different from the population density function discussed by most researchers. And a novel evolution equation, which is a nonhomogeneous parabolic type equation, is derived. From this, the stationary solution and the firing rate of the stationary states are given. Last, by the Fourier transform, the time dependent solution is also obtained. This method can be used to analyze the various dynamic behaviors of neuronal populations.

关 键 词：Analytic approach Neuronal population Dynamic model Fourier transform 

分 类 号：O175.2[理学—数学] C924.2[理学—基础数学]