Fractional-order PD Control at Hopf Bifurcations In a Neuron System

The problem of bifurcation control is investigated for a delayed neuron system under a novel fractional-order controller. Taking discrete delay as a bifurcation parameter, we use a novel fractional-order Proportional-Derivative (PD) feedback controller to adjust the control parameter, so as to analyse the stability and Hopf bifurcation of the system. The effect on the system bifurcation point is studied in comparison with an integer-order controller. The stability of the system is judged by the Routh-Hurwitz criteria. Through calculation and analysis, we derive sufficient conditions of ensuring Hopf bifurcation to occur for this model. Finally, numerical simulation examples are presented to show the feasibility of the theoretical results.