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Zbl 1177.34103
Saha, Tapan; Chakrabarti, Charugopal
Dynamical analysis of a delayed ratio-dependent Holling-Tanner predator-prey model. (English)
[J] J. Math. Anal. Appl. 358, No. 2, 389-402 (2009). ISSN 0022-247X

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.
[E. Ahmed (Mansoura)]

MSC 2000:: *34K60 Applications of functional-differential equations
92D25 Population dynamics
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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Zentralblatt MATH Berlin [Germany]