HOPF BIFURCATION ANALYSIS OF A FRACTIONAL-ORDER HOLLING–TANNER PREDATOR-PREY MODEL WITH TIME DELAY

Abstract

Abstract We study a fractional-order delayed predator-prey model with Holling–Tanner-type functional response. Mainly, by choosing the delay time $\tau $ as the bifurcation parameter, we show that Hopf bifurcation can occur as the delay time $\tau $ passes some critical values. The local stability of a positive equilibrium and the existence of the Hopf bifurcations are established, and numerical simulations for justifying the theoretical analysis are also presented.