一类具有阿利效应的离散特化捕食系统的动力学研究
Dynamical Analysis of a Discrete Specialist Predator System with the Allee Effect
摘要: 基于一个具有阿利效应和Holling I型功能的连续特化捕食模型，首先采用半离散化方法建立了一类离散特化捕食系统，并分析了系统平衡点的性质及其动力学行为。其次，将捕食者种群的食物转化系数作为分岔参数，分析了该参数变化对正平衡点稳定性的影响。研究表明，系统在参数达到临界条件时会发生Neimark-Sacker分岔并出现准周期解。最后，通过数值模拟验证了上述理论结果的有效性，进一步揭示了离散化模型在捕食者–食饵系统研究中的动态特征。
Abstract: Based on a continuous specialist predator model characterized by the Allee effect and a Holling type I functional response, a discrete-time analogue is constructed via a semi-discretization method. The local stability and dynamical properties of the equilibria are systematically analyzed. Considering the predator’s food conversion factor as the bifurcation parameter, the effect of its variation on the stability of the positive equilibrium is analyzed in detail. The analysis demonstrates that a Neimark-Sacker bifurcation occurs when the bifurcation parameter reaches a critical value, leading to the emergence of quasiperiodic solutions. Finally, numerical simulations are further conducted to confirm the theoretical predictions and to highlight the dynamic features inherent in the discrete predator-prey model.
文章引用：乔明慧, 孙福芹. 一类具有阿利效应的离散特化捕食系统的动力学研究[J]. 应用数学进展, 2025, 14(12): 373-384. https://doi.org/10.12677/aam.2025.1412514

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