A stochastic chemostat model with an inhibitor and noise independent of population sizes

Shulin Sun and Xiaolu Zhang

Physica A: Statistical Mechanics and its Applications, 2018, vol. 492, issue C, 1763-1781

Abstract: In this paper, a stochastic chemostat model with an inhibitor is considered, here the inhibitor is input from an external source and two organisms in chemostat compete for a nutrient. Firstly, we show that the system has a unique global positive solution. Secondly, by constructing some suitable Lyapunov functions, we investigate that the average in time of the second moment of the solutions of the stochastic model is bounded for a relatively small noise. That is, the asymptotic behaviors of the stochastic system around the equilibrium points of the deterministic system are studied. However, the sufficient large noise can make the microorganisms become extinct with probability one, although the solutions to the original deterministic model may be persistent. Finally, the obtained analytical results are illustrated by computer simulations.

Keywords: Stochastic chemostat model; Inhibitor; Itô formula; Lyapunov function; Asymptotic behavior (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:492:y:2018:i:c:p:1763-1781

DOI: 10.1016/j.physa.2017.11.096

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