含分布时滞和Allee效应的单物种模型的动力学分析
Dynamical Analysis of a Single Species Model with Distributed Delay and Allee Effect

生物数学作为生物学与数学的交叉学科，旨在挖掘数学工具在生命科学中的应用潜力，并通过构建数学模型解决生物学问题。基于微分方程的单种群动态模型研究是该领域的重要方向之一。在此基础上，我们结合常微分方程理论、定性分析和非线性系统技术，设计了一种包含分布时滞和Allee效应的Logistic型种群模型。通过对系统结构与动力学行为的深入分析，我们阐明了模型在边界稳定状态下的规律，并给出了平衡状态及其维持条件。
Biomathematics, as an interdisciplinary field combining biology and mathematics, aims to explore the potential of mathematical tools in the life sciences and solve biological problems by constructing mathematical models. The study of single-population dynamic models based on differential equations is one of the key directions in this field. Building on this foundation, we have developed a Logistic-type population model incorporating distributed delays and the Allee effect by integrating the theory of ordinary differential equations, qualitative analysis, and nonlinear system techniques. Through an in-depth analysis of the system’s structure and dynamic behavior, we elucidate the patterns of the model under boundary stability and provide the equilibrium states along with their maintenance conditions.