DYNAMICS OF FRACTIONAL-ORDER PREDATOR–PREY MODEL INCORPORATING TWO DELAYS

Abstract

This paper studies the problem of bifurcation for a fractional-order predator–prey system with two different delays by considering fractional interval [Formula: see text]. Multiple delays-depended stability domains of the developed model are procured and the bifurcation points are exactly established by taking advantage of two different delays as bifurcation parameters, respectively. It detects that the stability performance can be extremely varied with the changes of control parameter upon one delay is established. System possesses excellent stability performance when choosing the smaller control parameter, and Hopf bifurcation emerges from system once control parameter passes through the critical values, which degrades the performance of the system. Numerical simulations are finally performed to check our theoretical analysis.