Dynamical analysis of a delayed ratio-dependent Holling-Tanner predator-prey model |
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| Authors: | Tapan Saha Charugopal Chakrabarti |
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| Affiliation: | a Department of Mathematics, Haldia Government College, East Midnapore 721657, India
b Department of Applied Mathematics, University of Calcutta, Kolkata 700009, India |
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| 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. |
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| Keywords: | Holling-Tanner model Ratio-dependent response Time delay Hopf-bifurcation Blow up transformation Lyapunov function Global asymptotic stability |
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