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Zbl 1243.34119
Zhang, Jia-Fang
Bifurcation analysis of a modified Holling-Tanner predator-prey model with time delay. (English)
[J] Appl. Math. Modelling 36, No. 3, 1219-1231 (2012). ISSN 0307-904X

Summary: A modified Holling-Tanner predator-prey model with time delay is considered. By regarding the delay as the bifurcation parameter, the local asymptotic stability of the positive equilibrium is investigated. Meanwhile, we find that the system can also undergo a Hopf bifurcation of nonconstant periodic solution at the positive equilibrium when the delay crosses through a sequence of critical values. In particular, we study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions, an explicit algorithm is given by applying the normal form theory and the center manifold reduction for functional differential equations. Finally, numerical simulations supporting the theoretical analysis are also included.

MSC 2000:: *34K60 Applications of functional-differential equations
34K18 Bifurcation theory of functional differential equations
92D25 Population dynamics

Keywords: predator-prey model; delay stability; Hopf bifurcation; periodic solution

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