title: Competition in the chemostat: A stochastic multi-species model and its asymptotic behavior.
abstract: 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.
authors.affiliation: School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China.
authors.forename: Chaoqun
authors.initials: C
authors.lastname: Xu
authors.affiliation: College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China. Electronic address: sanling@usst.edu.cn.
authors.forename: Sanling
authors.initials: S
authors.lastname: Yuan
mesh_terms: D017753:Ecosystem; D008954:Models, Biological; D013269:Stochastic Processes
keywords: Competitive exclusion principle; Stochastic break-even concentration; Stochastic chemostat model