一类捕食–食饵随机微分模型的灭绝与持久性分析
Analysis of Extinction and Persistence in a Stochastic Predator-Prey Model
摘要: 本文提出并研究了一类三物种捕食–食饵模型，该模型在经典Lotka-Volterra结构基础上引入了白噪声干扰以模拟环境波动的影响。通过构造李雅普诺夫函数并结合R.Z. Khasminskii稳定性理论，我们分析了不同噪声强度对系统中各类种群的持久性与灭绝性的影响，得到了物种灭绝与持久的充分或必要条件。理论的结果得到了数值模拟的支持。
Abstract: This paper proposes and investigates a three-species predator-prey model, which introduces white noise disturbances into the classical Lotka-Volterra structure to simulate the effects of environmental fluctuations. By constructing Lyapunov functions and employing R.Z. Khasminskii-type stability theory, we analyze the influence of different noise intensities on the persistence and extinction of various populations within the system, deriving sufficient or necessary conditions for species extinction and persistence. The theoretical findings are supported by numerical simulations.
文章引用：常蔚, 廖新元. 一类捕食–食饵随机微分模型的灭绝与持久性分析[J]. 应用数学进展, 2025, 14(10): 126-137. https://doi.org/10.12677/aam.2025.1410426

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