Stability and Bifurcation Control in a Fractional Predator–Prey Model via Extended Delay Feedback

Abstract

This paper explores the bifurcation control of a fractional predator–prey system with an active extended delayed feedback controller. Delay-induced bifurcations criteria for such an uncontrolled system are firstly derived by selecting time delay as a bifurcation parameter. Then, an extended delayed feedback controller is cleverly devised to control Hopf bifurcation for the proposed system. It means that the bifurcation dynamics can be efficaciously controlled for a given system with the adjustment of the fractional order, feedback gain and extended feedback delay provided that the remnant parameters are fixed. The obtained results significantly extend the preceding studies concerning bifurcation control of delayed fractional-order systems. To verify the correctness of the established theory, some numerical results are presented.