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Dynamical analysis of a delayed ratio-dependent Holling-Tanner predator-prey model. (English) Zbl 1177.34103
Authors’ abstract: 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 $\left(0,0\right)$ 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.
##### MSC:
 34K60 Qualitative investigation and simulation of models 92D25 Population dynamics (general) 34K25 Asymptotic theory of functional-differential equations 34K18 Bifurcation theory of functional differential equations 34K20 Stability theory of functional-differential equations