In this paper, a Beddington-DeAngelis amensalism system with weak Allee effect on the first species are introduced and investigated. The existence and stability of all possible trivial, semi-trivial and interior equilibria of the model are studied. By utilizing Sotomayor’s theorem, bifurcation analysis has been proposed and obtain one saddle-node bifurcation. Furthermore, in view of Poincaré transformation, the behaviors near infinity and the nonexistence of close orbits are obtained and lead to the presentation of all possible global phase portraits. The global phase portrait in \(R_{5}\) with two stable node \(E_{2}\) and \(E_{1}^{*}\) is a new case due to the appearance of bistable structure. Finally, some numerical examples are offered to verify and extend the analytical results and visualize the interesting phenomenon.

本文介绍并研究了对第一个物种具有弱Allee效应的Beddington-DeAngelis闭经系统。研究了模型所有可能的平凡，半平凡和内部均衡的存在性和稳定性。利用索托马约尔定理，提出了分叉分析方法，并获得了一个鞍节点分叉。此外，鉴于庞加莱变换，可以获得接近无限的行为和不存在近轨道的行为，并导致呈现所有可能的全局相位肖像。\（R_ {5} \）中具有两个稳定节点\（E_ {2} \）和\（E_ {1} ^ {*} \）的全局相位肖像由于双稳态结构的出现，这是一个新案例。最后，提供了一些数值示例，以验证和扩展分析结果并可视化有趣的现象。