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Stability Analysis of An Annular Neural Network with Time-Delay Control

Abstract: In this paper, an annular neural network model with three neurons and delays is considered. Time delay can be regard as a<br />source of instability, so that regarding the time-delay \tao 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.