BIFURCATION IN A TWO-DIMENSIONAL NEURAL NETWORK MODEL WITH DELAY  

作　　者：魏俊杰 张春蕊 李秀玲 

机构地区：[1]DepartmentofMathematics,HarbinInstituteofTechnology,Harbin150001,P.R.China [2]KeyLaboratoryofForestryPlantEcologyofMinistryofEducation,NortheastForestryUniversity,Harbin150040,P.R.China [3]DepartmentofBasicScienceandArt,ChangchunTaxationCollege,Changchun130022,P.R.China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2005年第2期210-217,共8页应用数学和力学（英文版）

基　　金：theNationalNaturalScienceFoundationofChina ( 1 983 1 0 3 0 )

摘　　要：A kind of 2-dimensional neural network model with delay is considered. By analyzing the distribution of the roots of the characteristic equation associated with the model, a bifurcation diagram was drawn in an appropriate parameter plane. It is found that a line is a pitchfork bifurcation curve. Further more, the stability of each fixed point and existence of Hopf bifurcation were obtained. Finally, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were determined by using the normal form method and centre manifold theory.A kind of 2-dimensional neural network model with delay is considered. By analyzing the distribution of the roots of the characteristic equation associated with the model, a bifurcation diagram was drawn in an appropriate parameter plane. It is found that a line is a pitchfork bifurcation curve. Further more, the stability of each fixed point and existence of Hopf bifurcation were obtained. Finally, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were determined by using the normal form method and centre manifold theory.

关 键 词：neural network centre manifold pitchfork bifurcation Hopf bifurcation 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程] O32[自动化与计算机技术—控制科学与工程]