一类具有随机环境扰动的捕食者–食饵生态模型动力学问题研究
Research on Dynamics of a Predator-Prey Ecological Model with Stochastic Environmental Disturbances
摘要: 本文提出了一类带有随机环境扰动的捕食者–食饵种群生态模型，对其特定动力学行为进行理论分析与数值模拟。数学理论工作集中讨论了模型解的全局正性、随机最终有界性，同时分析了种群灭绝、持久生存和系统稳态分布的充分条件。数值模拟结果发现，环境白噪声强度是影响捕食者和食饵种群存活与灭绝的关键因素，从概率动力学的角度揭示了种群生长共存模式及其内在驱动机制，为拓宽捕食生态模型复杂动力学问题的研究框架提供一定的理论支撑。
Abstract: In this paper, we proposed a predator-prey population ecological model with stochastic environ- mental disturbances, and conducted theoretical analysis and numerical simulation of its specific dynamic behavior. The mathematical theory work focused on the global positivity and stochastic ultimate boundedness of model solutions, and analyzed the sufficient conditions for population extinction, persistent survival, and system steady-state distribution. Numerical simulations revealed that the intensity of environmental white noise was a key factor affecting the survival and extinction of both predator and prey populations. From the perspective of probabilistic dynamics, this study uncovered the population growth coexistence mode and their intrinsic driving mechanisms, which could provide some theoretical support for expanding the research framework of complex dynamical problems in predator-prey ecological models.
文章引用：林绍奇, 方靖哲, 俞诚杨, 孙逞阳, 赵柄皓, 邓静茹, 于恒国. 一类具有随机环境扰动的捕食者–食饵生态模型动力学问题研究[J]. 应用数学进展, 2026, 15(3): 273-293. https://doi.org/10.12677/aam.2026.153105

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