Hopf bifurcation analysis of a fractional order Holling-Tanner predator-prey model with time delay

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.

doi:https://doi.org/10.1017/S1446181122000025