Xu Chaoqun, Yuan Sanling
School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China.
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China.
Math Biosci. 2016 Oct;280:1-9. doi: 10.1016/j.mbs.2016.07.008. Epub 2016 Jul 27.
In this paper, a stochastic chemostat model in which n-species compete for a single growth-limiting substrate is considered. We first prove that the stochastic model has an unique global positive solution by using the comparison theorem for stochastic differential equations. Then we show that when the noise intensities are small, the competition outcome in the chemostat is completely determined by the species' stochastic break-even concentrations: the species with the lowest stochastic break-even concentration survives and all other species will go to extinction in the chemostat. In other words, the competitive exclusion principle holds for stochastic competition chemostat model when the noise intensities are small. Moreover, we find that noise may change the destiny of the species. Numerical simulations illustrate the obtained results.
本文考虑了一个n物种竞争单一生长限制底物的随机恒化器模型。我们首先利用随机微分方程的比较定理证明该随机模型有唯一的全局正解。然后我们表明，当噪声强度较小时，恒化器中的竞争结果完全由物种的随机盈亏浓度决定：随机盈亏浓度最低的物种存活，而所有其他物种将在恒化器中灭绝。换句话说，当噪声强度较小时，随机竞争恒化器模型的竞争排斥原理成立。此外，我们发现噪声可能改变物种的命运。数值模拟说明了所得到的结果。
