In this paper, we develop a population equation based on the Ricker model with periodic carrying capacity and embedded mechanisms of both weak and strong types of Allee effect: We prove a persistence property and existence of periodic solutions in each case of Allee effect. We find sufficient conditions for the periodic solution to be globally asymptotically stable and sufficient conditions for this solution to become unstable. We show that the mechanism of weak Allee effect increases the range of stability for the periodic solution.

中文翻译：

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具有可变 Allee 效应和周期性承载能力的差分人口方程

在本文中，我们开发了基于 Ricker 模型的人口方程，该模型具有周期性承载能力和弱和强类型 Allee 效应的嵌入机制：我们证明了 Allee 效应的每种情况下的持久性和周期性解的存在。我们找到了使周期解全局渐近稳定的充分条件和使该解变得不稳定的充分条件。我们表明弱 Allee 效应的机制增加了周期解的稳定性范围。