Dynamic Analysis Of Two Kinds Of Neural Networks With Time Delay

In recent years,neural network has been widely used in signal and image processing,pattern recognition,artificial intelligence and combinatorial optimization,which has attracted people's attention on its dynamic properties.In the process of information transmission,there are inevitably time delays that affect the dynamic behavior of neural networks.Therefore,the dynamic analysis of neural networks with time delay has become a hot topic.In this paper,we studied two kinds of common neural network models with time-delay,and analyzed the four-dimensional feedforward neural network and coupling neural network with time-delay and summarized relating research works.Firstly,the bifurcation of a class of four-dimensional feedforward neural networks with time delay is analyzed.According to the corresponding characteristic equation of the system at the equilibrium point,the conditions of Fold bifurcation and Hopf bifurcation of the system could be determined.By using the central manifold theory and the normal form method,we could be obtained separately that the normal form of the Fold bifurcation and the Hopf bifurcation of the system on the central manifold.The normal form of Fold bifurcation would generate pitchfork bifurcation and transitional bifurcation in different situations,and drawing corresponding bifurcation diagrams.According to the formula for calculating the stability of periodic solution of Hopf bifurcation,the direction of bifurcation and the stability of periodic solution are determined,and the rationality of the theory was proved by numerical simulation.Then,the dynamic properties of the Hopf-pitchfork bifurcation are studied for two-neuron delay coupled network model.By analyzing its characteristic equation,the existence of Hopf-pitchfork bifurcation is determined and its normal form is calculated.Then bifurcation diagrams and phase diagrams of the system were obtained,and generation of various phenomena in the bifurcation diagrams of the model were verified by numerical simulation.