Stability and bifurcation control of a neuron system under a novel fractional-order PD controller

In this paper, we address the problem of bifurcation control for a delayed neuron system. By introducing a new fractional-order Proportional-Derivative (PD) feedback controller, this paper aims to control the stability and Hopf bifurcation through adjusting the control gain parameters. The order chosen in PD controller is different with that of the integer-order neuron system. Sufficient conditions for guaranteeing the stability and generating Hopf bifurcation are constructed for the controlled neuron system. Finally, numerical simulation results are illustrated to verify our theoretical derivations and the relationships between the onset of the Hopf bifurcation and the gain parameters are obtained.