随机高斯捕食者-捕食者模型:噪音诱导的灭绝和不变性
Andrés Sanchéz1, Leon A Valencia1, Jorge M Ramirez Osorio2
1Instituto de Matemáticas, Universidad de Antioquia, Medellín, 050010, Antioquia, Colombia.
Mathematical biosciences and engineering : MBE
|September 3, 2025
概括
随机性可以导致捕食者-猎物模型的灭绝,即使确定性模型预测了共存. 这项研究分析了噪音引起的人口崩和生态系统的稳定性.
科学领域:
- 生态学
- 数学生物学
- 随机过程
背景情况:
- 斯的捕食者-猎物模型是一个基本的生态概念.
- 之前的研究通常假设不同的猎物动态或噪音类型.
- 了解随机性对人口稳定性的影响至关重要.
研究的目的:
- 在乘法高斯噪声下分析高斯捕食者-猎物模型与物流猎物动态和一般边界或亚线性功能响应.
- 建立模型定位的条件,确保解决方案的整体积极性和时刻性.
- 调查噪音引起的灭绝和静止分布的存在.
主要方法:
- 对模型正确位置的莱普诺夫型标准的推导.
- 分析随机微分方程以确定种群灭绝的条件.
- 确定已灭绝的种群的限制分布.
- 对特定功能反应 (霍林格型I) 的静止分布的研究.
主要成果:
- 对解决方案的整体积极性和时刻限度的明确标准.
- 证明随机性可以导致捕食者或猎物群体的灭绝,这与稳定的共存的决定性预测相矛盾.
- 建立了捕食者种群在灭绝的情况下的限制分布.
- 确定了足够的条件来证明霍林格I型功能反应的静止分布的存在和独特性.
结论:
- 复制高斯噪声可以破坏捕食者-猎物动态,导致不被确定性模型预测的灭绝.
- 这项研究提供了一个严格的数学框架来分析生态模型中的随机效应.
- 噪音强度对捕食者和猎物的长期行为和稳定性起着至关重要的作用.
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