PD Control at Hopf Bifurcations in a Neuron System with both Leakage and Distributed Delays

In this paper, a neural networks model with discrete and distributed delays is considered. For the sake of simplicity, a virtual neuron can be introduced to eliminate the influence of distributed delay, and a new equivalent system containing only one delay is obtained to study the bifurcation control problem of the initial neural network model with mixed delay. A PD controller is designed, and the leakage delay is used as the analysis variable. By analyzing the corresponding characteristic equations, the conditions for the existence of Hopf bifurcation are derived. In addition, the critical value is changed by regulating the control variable of PD feedback controller to achieve the desired dynamic behavior. The theoretical analysis is verified by numerical examples, and it is proved that the method can control the nonlinear dynamic behavior of the system.