Stability analysis of an annular neural network with time-delay control

In this paper, an annular neural network model with three neurons and delays is considered. Time delay can be regard as a source of instability, so that regarding the time-delay τ in feedback control as the bifurcation parameter, we construct a system and theoretically investigate the influence of time delays on linear stability and bifurcation. By analyzing the associated characteristic equation and applying the normal form theory, we obtain the direction of the Hopf bifurcation and the stability. Finally, an example is given and numerical simulations are represented to illustrate the obtained results of the proposed scheme.