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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.

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
Full Text: DOI
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