Abstract

In this paper, we propose a single species logistic model with feedback control and additive Allee effect in the growth of species. The basic aim of the paper is to discuss how the additive Allee effect and feedback control influence the above model’s dynamical behaviors. Firstly, the existence and stability of equilibria are discussed under three different cases, i.e., weak Allee effect, strong Allee effect, and the critical case. Secondly, we prove the occurrence of saddle-node bifurcation and transcritical bifurcation with the help of Sotomayor’s theorem. The above dynamical behaviors are richer and more complex than those in the traditional logistic model with feedback control. We find that both Allee effect and feedback control can increase the species’ extinction property. We also reveal some new bifurcation phenomena which do not exist in the single-species model with feedback control (Fan and Wang in Nonlinear Anal., Real World Appl. 11(4):2686–2697, 2010 and Lin in Adv. Differ. Equ. 2018:190, 2018).

中文翻译：

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具有加性Allee效应和反馈控制的单物种物流模型的稳定性和分岔。

摘要

在本文中，我们提出了一个具有反馈控制和加性Allee效应的单物种逻辑模型。本文的基本目的是讨论加性阿利效应和反馈控制如何影响上述模型的动力学行为。首先，在弱Allee效应，强Allee效应和临界情形三种情况下讨论了均衡的存在性和稳定性。其次，借助索托马约尔定理证明了鞍节点分叉和跨临界分叉的发生。与具有反馈控制的传统逻辑模型相比，上述动力学行为更加丰富和复杂。我们发现，Allee效应和反馈控制都可以增加物种的灭绝特性。2010年和Lin在高级顾问中。不同。等式 2018：190，2018）。