We present a continuous time predator-prey model and predator’s growth subjected to component Allee effect. The model also includes density dependent mortality of predator. We investigate our model both analytically and numerically, and highlighted the effect of density independent mortality and Allee effect. In our system, we find that a fixed point representing the extinction of predator is always a stable point. When coexistence equilibria exists our system is bistable. We have observed that tristability is possible for our model that includes two stable co-existence fixed point. The most important phenomena which we have observed are hydra effect and cascading effect. Due to component Allee effect in predator the system shows multiple hydra effect. We discuss the phenomenon of bubbling, which indicates increasing and decreasing of amplitudes of cycles. We have presented one-parametric as well as two-parametric bifurcation diagram and also all possible bifurcations that the system could go through.

我们提出了一个连续时间捕食者-猎物模型和捕食者的生长受到组件 Allee 效应的影响。该模型还包括捕食者的密度相关死亡率。我们从分析和数值上研究了我们的模型，并强调了与密度无关的死亡率和 Allee 效应的影响。在我们的系统中，我们发现代表捕食者灭绝的不动点总是一个稳定点。当共存平衡存在时，我们的系统是双稳态的。我们已经观察到，对于包含两个稳定共存不动点的模型，三稳态是可能的。我们观察到的最重要的现象是九头蛇效应和级联效应。由于捕食者中的组件 Allee 效应，该系统显示出多重九头蛇效应。我们讨论冒泡现象，这表明周期幅度的增加和减少。我们已经展示了单参数和双参数分岔图，以及系统可能经历的所有可能分岔。