Exploring bifurcation in a fractional-order predator-prey system with mixed delays

This work chiefly develops and discusses a fractional-order predator -prey model with distributed delay and discrete delay. Applying skilly an ap-propriate variable substitution, a novel equivalent form of the fractional-order predator-prey model with distributed delay and discrete delay is derived. By virtue of the stability theorem and bifurcation principle of fractional-order dynamical system, we establish a delay-independent stability and bifurcation criterion ensuring the stability and the onset of Hopf bifurcation for the in-volved predator-prey system. The role of the time delay in stabilizing system and controlling Hopf bifurcation of the considered fractional-order predator -prey model is displayed. Software simulation results are presented to support the key theoretical fruits.