具有HollingⅡ型功能性作用函数的随机恒化器模型的渐近性态  

Asymptotic properties of a stochastic chemostat model with HollingⅡ functional response

作　　者：王璐[1] 原三领[1] 张同华 

机构地区：[1]上海理工大学理学院,上海200093 [2]斯威本科技大学数学系,澳大利亚

出　　处：《高校应用数学学报（A辑）》2012年第4期379-389,共11页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11271260;11001212);上海市教委科研创新重点项目(13ZZ116)

摘　　要：考虑了一类营养的转化率受到随机噪声干扰,具有HollingⅡ型功能性反应函数的随机恒化器模型.通过构造Liapunov函数,利用停时、伊藤公式证明了模型正解的全局存在唯一性.研究了模型解的长期渐近性态,主要揭示在不同条件下模型的解围绕其相应确定性模型的各类平衡点的振荡行为.In this paper, a stochastic chemostat model with Holling II functional response and the nutrition conversion rate being influenced by white noise is considered. By constructing stochastic Liapunov function and using stopping time and Ito＇s formula, it is shown that there is an unique positive solution to the system with positive initial value. The long time behavior of the system is studied. Mainly, how the solution goes around the equilibriums of the corresponding deterministic system under different conditions is disclosed.

关 键 词：随机恒化器模型 白噪声 随机渐近稳定 伊藤公式 

分 类 号：O175[理学—数学]