具有弱Allee效应的捕食者—食饵模型动态

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

分析了一类食饵具有弱Allee效应的捕食者—食饵模型.给出了系统所有平衡点的分类和稳定性.利用Hopf分支的规范型理论,分析和数值模拟结果显示,Allee效应的加入可以导致系统产生一个稳定的极限环.结果表明,Allee效应可以破坏共存平衡点的稳定性,从而使以前简单的系统产生更丰富、复杂的动态行为,如超临界Hopf分支,这意味着Allee效应可能是捕食者—食饵群落周期波动的最简单的原因.

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.