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Dynamic behaviour of a delayed predator-prey model with harvesting. (English) Zbl 1215.92065
Summary: We analyze the dynamics of a delayed predator-prey system in the presence of harvesting. This is a modified version of the P. H. Leslie and J. C. Gower [Biometrika 47, 219–234 (1960; Zbl 0103.12502)] and Holling-type II scheme [C. S. Holling, Mem. Ent. Sec. Can. 45, 1–60 (1965)]. The main result is given in terms of local stability, global stability, influence of harvesting and bifurcation. Direction of Hopf bifurcation and the stability of bifurcating periodic solutions are also studied by using the normal form method and center manifold theorem.

MSC:
92D40 Ecology
34K20 Stability theory of functional-differential equations
34K18 Bifurcation theory of functional-differential equations
65C20 Probabilistic models, generic numerical methods in probability and statistics
34K13 Periodic solutions to functional-differential equations
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