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