保护生物多样性是全世界面临的重要难题，而有关种群动力学的研究则能为其提供科学的理论依据。其中种群系统的稳定性、分支及混沌等动态受到Allee效应的强烈影响，使之逐渐成为左右种群复杂动态的一个重要因素。本项目以经典的捕食-被捕食模型为基础，建立几类具有Allee效应的两种群系统，借助微分方程定性理论、种群动力学理论、动力系统分支和混沌的方法等，分析它们的动力学行为，探讨Allee效应对相应系统动力学的影响，以期获得Allee效应的形成机制及其对两种群动力学性态作用的一般规律; 同时总结普遍适用的研究方法，发展和丰富种群动力学理论; 此外，从生物学的角度解释理论分析与数值模拟的结果，为更好地保护生物多样性提供科学依据。

Biodiversity conservation is an important topic in the world, and the research on population dynamics can provide scientific theoretical basis for it. Allee effect, which is an important factor to control the complex dynamics of population, can strongly influence the stability, bifurcation and chaos of population systems. In this project, based on some classic predator-prey models, we will establish some population models with Allee effect. Applying qualitative theory of differential equation, population dynamics theory, the techniques of bifurcation and chaos from dynamical systems, we analyze the dynamic behavior of these systems with Allee effect to obtain the general principle of the impact of Allee effect on predator-prey systems. Meanwhile, we will derive the universally applicable research techniques for more generalized systems. Moreover, our results, including theoretical analysis and numerical simulation, may be applied to biology, and furtherly, they may provide scientific basis for biodiversity conservation in the future.