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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 $(0,0)$ 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.

MSC:
34K60Qualitative investigation and simulation of models
92D25Population dynamics (general)
34K25Asymptotic theory of functional-differential equations
34K18Bifurcation theory of functional differential equations
34K20Stability theory of functional-differential equations
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References:
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