具有比率型功能反应函数的随机恒化器系统的渐近性态

Asymptotic behavior of a stochastic ratio-dependent chemostat model

考虑到流出率受随机噪声的干扰,研究了一类具有比率型功能反应函数的随机恒化器系统,详细讨论了系统解的长期渐近性态。利用随机微分方程比较定理,证明了系统正解的全局存在惟一性。通过构造Lyapunov函数,利用It公式证明了系统的绝灭平衡点是全局随机渐近稳定的,研究了随机系统在确定性系统正平衡点附近解的渐近行为。

This paper studies the asymptotic behavior of a stochastic Chemostat model with ratio-dependent functional response in which the dilution rate was influenced by white noise. The long time behavior of the model is studied. There exists a unique positive solution by stochastic comparison theorem. Using Lyapunov function, we show the washout equilibrium is stochastically asymptotically stable in the large. Furthermore, we show how the solution spirals around the positive equilibrium of deterministic system.