Stability and Hopf bifurcation analysis of a tri-neuron BAM neural network with distributed delay

In this paper, a tri-neuron BAM neural network with distributed delay is considered. The distributed delay is regarded as the bifurcating parameter to study the dynamic behaviors in terms of local asymptotical stability and local Hopf bifurcation. By analyzing the associated characteristic equation, Hopf bifurcation occurs when the delay passes through a sequence of critical values. The direction and stability of bifurcating periodic solutions are also derived by the normal form theory and the center manifold theorem. Finally, an illustrative example is also given to support the theoretical results.