Dynamical Study Of A Neural Network Model With Time Delays

The studies on dynamics of delayed systems are reviewed in this paper. They concern mechanics,mechanical engineering,aeronautics and astronautics, ecology,biology,neural network,electronics,information technology,economics and so on.The typical methods and techniques are discussed.It is shown that the delayed systems are ubiquitous in nature and engineering.Then the paper reveals the dynamics of a delayed neural network of four neurons. It presents the detailed analysis on the stability and the stability switches of the network equilibrium first,and then on the Hopf bifurcation and the bifurcating periodic response.Many new problems and phenomena need to be studied and explored,when the effects of delays on systems are considered.Based on some existing problems in the studies,some topics for future studies are suggested,for examples,control strategies focused on delayed feedbacks,effects combining delay with nonlinearities on systems.These problems should be addressed since they do not occur in nonlinear systems without delays.