Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with time delays

Abstract

In this Letter, a four-neuron BAM neural network with four time delays is considered, where the time delays are regarded as parameters. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when these delays pass through a sequence of critical value. A formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions is given by using the normal form method and center manifold theorem.