Study of Bifurcation Phenomenon for Neural Network with Continuously Time Delay

In this paper, we study the Hopf bifurcation phenomena of a neural network with a continuous time delay. Using the average time delay as bifurcation parameter, we have proved that the model undergoes a sequence of Hopf bifurcations in both the strong kernel and weak kernel cases. Stability criteria for the bifurcating periodic solutions are derived in the neural network with weak kernel. Some numerical examples and the computer simulation results are also presented to justify the theoretical results.