具有Gauss白噪声和Lévy噪声的似然竞争模型分析

Analysis of a apparent competition model with Gauss white noise and Lévy noise

研究了一个带有食饵庇护的随机似然竞争模型,采用Gauss白噪声和Lévy噪声来模拟环境的随机扰动.通过利用比较定理和伊藤公式,得到了随机模型存在全局正解的结论以及种群灭绝、均值稳定、均值强持续生存的阈值条件.研究结果表明无论是Gauss白噪声还是Lévy噪声对于种群的持续生长都是不利的,因此建模时很有必要考虑环境的随机变化.

A stochastic apparent competition model with prey refuge is studied, Gauss white noise and Lévy noise is adopted to simulate the random perturbation of environment. By virtue of comparison theorem and It 's formula, the conclusion that the stochastic model has a global positive solution and the threshold conditions of extinction, stable in the mean, strong persistence in the mean for population are derived. The results show that whether Gauss white noise or Lévy noise is unfavorable for the sustainable growth of population, therefore, it is essential to consider the stochastic change of environment when constructing model.