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Saha, Tapan; Chakrabarti, Charugopal

Dynamical analysis of a delayed ratio-dependent Holling-Tanner predator-prey model. (English) Zbl 1177.34103

J. Math. Anal. Appl. 358, No. 2, 389-402 (2009).
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.
Reviewer: E. Ahmed (Mansoura)

Cited in 33 Documents

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
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

Keywords:

Holling-Tanner model; ratio-dependent response; time delay; Hopf-bifurcation; blow up transformation; Lyapunov function; global asymptotic stability
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\textit{T. Saha} and \textit{C. Chakrabarti}, J. Math. Anal. Appl. 358, No. 2, 389--402 (2009; Zbl 1177.34103)
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