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The Dynamics of a Predator-Prey Model with Weak Allee Effect

LIU Zhiguang;ZHANG Fengpan;YOU Chunxiao;Henan University Institute of Applied Mathematics;Henan University School of Mathematics and Statistics;  
This paper deals with a predator-prey model with a weak Allee effect on the prey population.The classification and stability of all equilibriums of the system are given.Using the normal form theory of Hopf bifurcation,it is shown that the Allee effect can result in the existence of a stable limit cycle.Our results suggest that the weak Allee effect can destabilize the coexistence equilibrium and bring the rich and complicated dynamics to the previous simple model,such as supercritical Hopf bifurcations,implying that the weak Allee effect can be one of the simplest reasons for periodic behavior in the predator-prey communities.
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