EXPLORING BIFURCATION IN A FRACTIONAL-ORDER PREDATOR-PREY SYSTEM WITH MIXED DELAYS
Changjin Xu, Dan Mu, Yuanlu Pan, Chaouki Aouiti, Lingyun Yao
Abstract
This work chiefly develops and discusses a fractional-order predatorprey model with distributed delay and discrete delay. Applying skilly an appropriate 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 involved predator-prey system. The role of the time delay in stabilizing system and controlling Hopf bifurcation of the considered fractional-order predatorprey model is displayed. Software simulation results are presented to support the key theoretical fruits.