Stability and Hopf bifurcation of a three-layer neural network model with delays

A kind of three-layer neural network with time delays is introduced. By analyzing its associated characteristic equation, local stability and the existence of Hopf bifurcation of the system are investigated. By using the normal form method and center manifold theorem, formulas to determine the direction of the Hopf bifurcation and the stability of bifurcating periodic solution are obtained. Numerical simulation results are also given to support our theoretical predictions.