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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.
MSC:
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