 Threshold dynamics of a chemostat model with Ornstein–Uhlenbeck process and single-species growth on two nutrientsMiaomiao Gao, Yanhui Jiang and Daqing Jiang Mathematics and Computers in Simulation (MATCOM), 2026, vol. 239, issue C, 917-949 Abstract: This paper aims to study the dynamic properties of a stochastic chemostat model with single-species growth on two perfectly substitutable nutrients, in which the maximal growth rates of the microorganisms satisfy the log-normal Ornstein–Uhlenbeck process. We first show the existence and uniqueness of the global positive solution. Then, sufficient condition for the extinction of the microorganisms is given. And by constructing suitable Lyapunov functions, we obtain the condition for the existence of stationary distribution, which implies the persistence of the microorganisms. We find that there is a threshold between persistence and extinction for the considered model. Moreover, the exact expression of the probability density function of the distribution is further derived. Finally, numerical simulations are provided to demonstrate the theoretical results. Keywords: Stochastic chemostat model; Log-normal Ornstein–Uhlenbeck process; Extinction; Stationary distribution; Density function (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:239:y:2026:i:c:p:917-949 DOI: 10.1016/j.matcom.2025.07.063 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.