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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 Magalh√£es. 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.

34K60Qualitative investigation and simulation of models
34K18Bifurcation theory of functional differential equations
37G05Normal forms
34K17Transformation and reduction of functional-differential equations and systems; normal forms
92D25Population dynamics (general)
34K13Periodic solutions of functional differential equations
34K20Stability theory of functional-differential equations
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