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Bifurcation analysis of a modified Holling-Tanner predator-prey model with time delay. (English) Zbl 1243.34119
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:
34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K18 Bifurcation theory of functional-differential equations
92D25 Population dynamics (general)
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