Qualitative Analysis About Aneural Network Model With Delay

Neuron network is a kind of intelligent control technology,which can simulate human being's intelligent behavior,solve many complicated and nondeterministic nonlinear automation problems not settled by traditional automation technology. Therefore,during the last several decades the study of neuron network has aroused the general interest of academic field,with special attention given to Professor Hopfield of California Institute of Technology,who put forward successive neuron network model.In a large sense the model's stability is connected with associative memory.so this article focuses on the study of the stability and periodic sollution of a binary form Hopfield model's equilibrium.In reference [10], the auther studies the periodic sollution of the model in the absence of time delay.Because time delay is inevitable in the process of information transfer, this article studies its influence on system dynamics behavior with time delay as the parameter. We find out that there is a change in the stability of system equilibrium when time delay T experiences certain variations,].e..when it changes from asymptotical stability(unstability) to unstability(stability), these T become the system's bifurcation value (the system has small-scale amplitude notrivial periodic sollution around these values). We also refer to the center manifold theorem and normal form theory, and list two calculation formulas which reflect the stability with Hop bifurcating periodic sollution, bifurcating direction.Thus provide a basis for numerical simulation calculation. Generally speaking, the Hop bifurcation thus obtained is local, which means that periodic sollution only exists within the narrow field of bifurcation value TO. Therefore. this article studies the existence of the global notrivial periodic sollution ( including all > ), which is of great importance in practice as well as in theory.