Exclusion and persistence in deterministic and stochastic chemostat models
type: Item
instance of: scholarly article
title: Exclusion and persistence in deterministic and stochastic chemostat models
zbMATH Open document ID: 1089.34041
author: Yanyan Li
published in: Journal of Differential Equations
publication date: 2005-10-24T00:00:00Z
review text: The authors first introduce and discuss a variant of the standard deterministic chemostat model. The principal difference is that microbe removal and growth rates depend on the biomass concentration with removal terms increasing faster than growth terms. In the single species scenario, they turn out that the qualitative behavior is virtually indistinguishable from the standard chemostat model. In the multiple species scenario, by using a comparison principle, they prove that persistence of all species is possible. Then, the authors turn to modelling the influence of random fluctuations by setting up and analyzing a stochastic differential equation. In the single species case, they show that if the deterministic counterpart admits persistence, and the stochastic effects are not too strong, then there are a recurrent system and, with some additional assumptions, the stochastic solution can be expected to remain close to the interior deterministic stationary point. In the two species case, they prove a transient result and show that under certain conditions, the stochastic model leads to extinction even though the deterministic counterpart predicts persistence.
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 2217409
zbMATH Keywords: deterministic chemostat model
zbMATH Keywords: stochastic differential equation
zbMATH Keywords: exclusion
zbMATH Keywords: persistence
reviewed by: Wan-Tong Li
MaRDI profile type: Publication
full work available at URL: j.jde.2005.06.017
OpenAlex ID: W1985300928
cites work: Criteria for recurrence and existence of invariant measures for multidimensional diffusions
cites work: A Mathematical Model of the Chemostat with a General Class of Functions Describing Nutrient Uptake
cites work: Stochastic Calculus
cites work: Competition in the Chemostat: Global Asymptotic Behavior of a Model with Delayed Response in Growth
cites work: Persistence criteria for a chemostat with variable nutrient input
cites work: Stochastic evolutionary game dynamics
cites work: Microbial Competition
cites work: Q4086524
cites work: Evolutionary dynamics with aggregate shocks
cites work: Q4510664
cites work: A new Liapunov function for the simple chemostat
cites work: Q4296601
cites work: Limiting Behavior for Competing Species
cites work: A Mathematical Theory for Single-Nutrient Competition in Continuous Cultures of Micro-Organisms
cites work: A comparison theorem for solutions of stochastic differential equations and its applications
cites work: The long-run behavior of the stochastic replicator dynamics
cites work: Q4002114
cites work: On comparison systems for ordinary differential equations
cites work: Optimal Discounted Stochastic Control for Diffusion Processes
cites work: Global Asymptotic Behavior of the Chemostat: General Response Functions and Different Removal Rates
cites work: Some mathematical problems concerning the ecological principle of competitive exclusion
cites work: The Theory of the Chemostat
cites work: A stochastic analysis of the growth of competing microbial populations in a continuous biochemical reactor
cites work: Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations
cites work: Competition in the Chemostat: A Distributed Delay Model and Its Global Asymptotic Behavior
cites work: A system of resource-based growth models with two resources in the unstirred chemostat
DOI: 10.1016/J.JDE.2005.06.017
description: scientific article