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The effects of harvesting and time delay on predator-prey systems with Holling type II functional response. (English) Zbl 1203.34137

Two predator-prey models with delayed predator specific growth and Holling type II functional response are studied using a normal form technique developed by Faria and Magalhães. For the model with a constant prey harvesting, Hopf bifurcations occur as the delay crosses the critical values. The direction and the stability of the bifurcating periodic solutions are determined. For the model with a constant predator harvesting, Bogdanov-Takens bifurcations are demonstrated and a complete bifurcation diagram is obtained. Numerical simulations are performed to support the theoretical results.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K18 Bifurcation theory of functional-differential equations
37G05 Normal forms for dynamical systems
34K17 Transformation and reduction of functional-differential equations and systems, normal forms
92D25 Population dynamics (general)
34K13 Periodic solutions to functional-differential equations
34K20 Stability theory of functional-differential equations
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