Sharp conditions for the existence of a stationary distribution in one classical stochastic chemostat

Dianli Zhao and Sanling Yuan

Applied Mathematics and Computation, 2018, vol. 339, issue C, 199-205

Abstract: This paper studies the asymptotic behaviors of one classical chemostat model in a stochastic environment. Based on the Feller property, sharp conditions are derived for the existence of a stationary distribution by using the mutually exclusive possibilities known in [11, 12] (See Lemma 2.4 for details), which closes the gap left by the Lyapunov function. Further, we obtain a sufficient condition for the extinction of the organism based on two noise-induced parameters: an analogue of the feed concentration S* and the break-even concentration λ. Results indicate that both noises have negative effects on persistence of the microorganism.

Keywords: Stochastic chemostat model; Feller property; Stationary distribution; Extinction; Break-even concentration (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:339:y:2018:i:c:p:199-205

DOI: 10.1016/j.amc.2018.07.020

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