污染环境下一类随机三种群捕食系统阈值的分析

The threshold analysis for stochastic three species predator-prey model in a polluted environment

阈值普遍存在于自然生态系统中,阈值的研究对自然资源保护和生态系统可持续管理具有重要的理论和实践意义。本文研究污染环境下两食饵一捕食者随机三种群捕食模型,运用伊藤微分法则、积分定理、积分中值定理、随机比较定理以及线性代数的相关理论,获得了各种群趋于局部灭绝、随机非平均持久及随机弱平均持久的充分条件,随之得到在一定条件下种群x_1(t),x_2(t)及x_3(t)的随机弱平均持久与趋于灭绝之间的阈值分别为:γ_(10)-α_1~2/2-γ_(11)〈C_0〉*,Δ_2-_2〈C_0〉*,A_3-_3〈C_0〉*。

Threshold is generally exists in the natural ecosystem, so the study of threshold value has an important theoreticaland practical significance for thenatural resources protection and ecological system of sustainable management. In this paper, westudy two-predator one-prey model of stochastic three species in a polluted environment. By using Ito formula, integrationtheorem, mean value theorem of integrals, stochastic comparison theorem and the related theory of linear algebra, sufficientconditions for extinction,nonpersistent in the mean a.s. and weak persistence in the mean a.s. are obtained. Then, we obtained that, in some certain conditions,γ10-α^21/2-γ11（C0）＊,Δ2-Δ2（C0）＊,A3-A3（C0）＊respectively, the threshold between the stochastic weak persistence in the mean and extinction of x1（t）,x2（t）and x3（t）