Bifurcation control of a fractional-order PD control strategy for a delayed fractional-order prey–predator system

A fractional-order proportional-derivative controller is constructed to give control over the bifurcation of a delayed fractional-order prey–predator system. Firstly, selecting time delay as the bifurcation variable, we investigate the proper equation of the proposed system. Then, some stability conditions of the equilibrium and critical values of Hopf bifurcation are gained. Results show that the proposed controller is successful in deferring the arise of the Hopf bifurcation via setting proper control parameters. Additionally, the correlation between the Hopf bifurcation point and the fractional order is illustrated. Lastly, a numeric example is carried out to verify our major results.