BIFURCATION-ANALYSIS OF A NEURAL NETWORK MODEL

被引:100
作者
BORISYUK, RM
KIRILLOV, AB
机构
[1] UNIV TEXAS,SW MED CTR,DEPT CELL BIOL & NEUROSCI,5323 HARRY HINES BLVD,DALLAS,TX 75235
[2] ACAD SCI USSR,CTR RES COMP,PUSHCHINO 142292,USSR
基金
英国生物技术与生命科学研究理事会;
关键词
D O I
10.1007/BF00203668
中图分类号
TP3 [计算技术、计算机技术];
学科分类号
0812 ;
摘要
This paper describes the analysis of the well known neural network model by Wilson and Cowan. The neural network is modeled by a system of two ordinary differential equations that describe the evolution of average activities of excitatory and inhibitory populations of neurons. We analyze the dependence of the model's behavior on two parameters. The parameter plane is partitioned into regions of equivalent behavior bounded by bifurcation curves, and the representative phase diagram is constructed for each region. This allows us to describe qualitatively the behavior of the model in each region and to predict changes in the model dynamics as parameters are varied. In particular, we show that for some parameter values the system can exhibit long-period oscillations. A new type of dynamical behavior is also found when the system settles down either to a stationary state or to a limit cycle depending on the initial point.
引用
收藏
页码:319 / 325
页数:7
相关论文
共 28 条
[21]  
KUZNETSOV UA, 1983, FORTRAN ALGORITHMS P
[22]  
Levitin V. V., 1989, TRAX SIMULATION ANAL
[23]   CHAOTIC DYNAMICS OF INFORMATION-PROCESSING WITH RELEVANCE TO COGNITIVE BRAIN FUNCTIONS [J].
NICOLIS, JS .
KYBERNETES, 1985, 14 (03) :167-172
[24]  
SBITNEV VI, 1982, MEMORY LEARNING MECH
[25]   A MODEL FOR NEURONAL OSCILLATIONS IN THE VISUAL-CORTEX .1. MEAN-FIELD THEORY AND DERIVATION OF THE PHASE EQUATIONS [J].
SCHUSTER, HG ;
WAGNER, P .
BIOLOGICAL CYBERNETICS, 1990, 64 (01) :77-82
[26]  
SHIMIZU H, 1988, DYNAMIC PATTERNS COM
[27]  
WILSON HR, 1972, BIOPHYS J, V12, P2
[28]  
ZARHIN YG, 1978, FORTRANN ALGORITHMS