Hopf Bifurcation, Two Types Of High-dimensional Time Delay Neural Network Model

In this paper,the Hopf bifurcation of two higher dimensional neuron-network dynamical systems are studied on the basic of ODE's bifurcated theory.From the background of neuron-network,an n-dimension neuron-network model with constant delays is discussed by the high-dimension bifurcated theory and D-division theorem when the delays areτ1,…,τn and the bifurcated parameter is transmit coefficients b= bij(i, j=1,…, n),and an n-dimension neuron-network model with constant and continuous delays is also researched when the bifur-cated parameter is delayτ;then the direction and stability of bifurcated space pe-riodic solutions are investigated by center manifold theorem and normal formed theory. The condition of local Hopf bifurcation in high-dimension are obtained and the graphics for 3 and 4 Dimension are given by Matlab Software stimu-lation.The innovations have been done for Junjie Wei whose achievements were researched on 2-Dimension model with two constant delays and a few expansions and improvements have been accomplished on the basic of Hsu,Amirhossein H,Baoxian Wang who had studied on 2,3,4-Dimension model with contin-uous delays,some new conclusions are acquired for complex delayed model in n dimension,it can be reflected how every neuron move with special and general delays,or constant and continuous delays.As a result,this is more corresponded to the complexity and practical meaning for neuron sport.