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The impact of Allee effect on a predator-prey system with Holling type II functional response. (English) Zbl 1202.92088
Summary: The Allee effect is incorporated into a predator-prey model with Holling type II functional response. Compared with the predator-prey model without Allee effect, we find that the Allee effect of the prey species increases the extinction risk of both predators and prey. When the handling time of predators is relatively short and the Allee effect of the prey species becomes strong, both predators and prey may become extinct. Moreover, it is shown that the model with Allee effect undergoes Hopf bifurcations and heteroclinic bifurcations. The Allee effect of the prey species can lead to unstable periodical oscillations. It is also found that the positive equilibrium of the model could change from stable to unstable, and then to stable when the strength of Allee effect or the handling time of the predators increases continuously from zero, that is, the model admits stability switches as a parameter changes. When the Allee effect of prey species becomes strong, longer handling time of predators may stabilize the coexistent steady state.

##### MSC:
 92D40 Ecology 34C60 Qualitative investigation and simulation of models (ODE) 34D20 Stability of ODE 37N25 Dynamical systems in biology
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