Dynamical analysis of a delayed ratio-dependent Holling–Tanner predator–prey model

Abstract

In this paper, a delayed Holling–Tanner predator–prey model with ratio-dependent functional response is considered. It is proved that the model system is permanent under certain conditions. The local asymptotic stability and the Hopf-bifurcation results are discussed. Qualitative behaviour of the singularity $(0,0)$ is explored by using a blow up transformation. Global asymptotic stability analysis of the positive equilibrium is carried out. Numerical simulations are presented for the support of our analytical findings.