具有状态切换和跳跃的随机捕食–食饵模型的种群动态行为
Population Dynamical Behaviors of Stochastic Predator-Prey Models with Regime Switching and Jumps
DOI: 10.12677/aam.2025.143128, PDF,   
作者: 黄圆圆：中国地质大学(武汉)数学与物理学院，湖北 武汉
关键词: 捕食者–食饵模型；机制转换；Lévy跳跃；阈值；白噪声；Predator-Prey Models； Regime Switching； Lévy Jumps； Threshold； White Noise
摘要: 本文研究了一个具有Lévy跳跃噪声和马尔科夫切换的随机捕食者–食饵模型。与现有方法不同，本文引入了更精确的阈值用于分析捕食者与食饵种群的随机持久性和灭绝性，从而得出了有关物种存在性的充分且几乎必要条件。值得注意的是本文提出的阈值在理论证明下只取决于系统中的已知参数。最后，本文进行数值模拟，论证相关理论结果。
Abstract: In this paper, we study a stochastic predator-prey model with Lévy jump noise and Markov switching. Differently from the existing methods, more accurate thresholds are introduced for the analysis of the stochastic permanence and extinction of the population, which yields some sufficient and almost necessary conditions. It is worth noting that the thresholds proposed in this paper depend only on the known parameters in the system under the theoretical proof. Finally, the paper performs numerical simulations to demonstrate the relevant theoretical results.
文章引用：黄圆圆. 具有状态切换和跳跃的随机捕食–食饵模型的种群动态行为[J]. 应用数学进展, 2025, 14(3): 409-421. https://doi.org/10.12677/aam.2025.143128

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