Stability and Bifurcation Mechanism Analysis of a Three-Layer Fractional Neural Network with Multiple Delays

At present, most of the researches on neural network dynamics are focusing on simple networks with single-layer structure. Nevertheless, it should be noted that the actual neural network has the characteristics of multi-layer and multi-coupling. In this paper, a three-layer fractional-order neural network with multiple delays is proposed for the first time. By selecting time delay as the bifurcation parameter, the criteria of stability are analyzed and the conditions of Hopf bifurcation are given. Finally, file validity of theoretical research is verified by computer simulation. The results show that Hopf bifurcation occurs when the delay exceeds the bifurcation threshold. In addition, it is also found that fractional order have important effects on stability and Hopf bifurcation of non-integer order neural network.