随机高斯捕食者-猎物模型:噪声引起的灭绝和不变性

Leon Alexander Valencia, Ph. D, Jorge Mario Ramirez Osorio, Jorge Andres Sanchez
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摘要

本文探讨了一个具有有界或亚线性功能响应的随机高斯捕食者-猎物模型。该模型由随机微分方程系统描述,捕捉了随机波动对捕食者-猎物动力学的影响,尤其关注种群的稳定性、灭绝和存续。我们提供了解的存在性和有界性的充分条件,分析了噪声诱发的灭绝事件,并研究了霍林 I 型功能响应情况下唯一静态分布的存在性。我们的分析凸显了噪声在决定长期生态结果中的关键作用,表明即使在确定性模型预测稳定共存的情况下,随机噪声也会导致种群灭绝或显著改变系统的动态。
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The Stochastic Gause predator-prey model: noise-induced extinctions and invariance
This paper explores a stochastic Gause predator-prey model with bounded or sub-linear functional response. The model, described by a system of stochastic differential equations, captures the influence of stochastic fluctuations on predator-prey dynamics, with particular focus on the stability, extinction, and persistence of populations. We provide sufficient conditions for the existence and boundedness of solutions, analyze noise-induced extinction events, and investigate the existence of unique stationary distributions for the case of Holing Type I functional response. Our analysis highlights the critical role of noise in determining long-term ecological outcomes, demonstrating that even in cases where deterministic models predict stable coexistence, stochastic noise can drive populations to extinction or alter the system's dynamics significantly.
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