Journal
CHAOS SOLITONS & FRACTALS
Volume 153, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2021.111585
Keywords
Random chemostat model; Ornstein-Uhlenbeck process; Forward attractors; Random dynamical system; Long-time behavior
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Funding
- National Natural Science Foundation of China [12171039, 11771044, 11871007]
- Fundamental Research Funds for the Central Universities [2021NTST03]
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This paper investigates a stochastic chemostat model with multiplicative noise, proving the existence and uniqueness of global positive solutions and discussing the impact of forward absorbing sets and forward attracting sets on the long-term behavior of microorganisms. Comparison between different ways of modeling randomness in the chemostat model is conducted, supported by numerical simulations.
In this paper, we consider a stochastic chemostat model with multiplicative noise. By appropriate variable substitution, we get a random chemostat system driven by Ornstein-Uhlenbeck process, which will no longer contain white noise. Firstly, we prove the existence and uniqueness of the global positive solution for any positive initial value for random chemostat system. Secondly, we state some results regarding the existence of a compact forward absorbing set as well as a forward attracting one, its internal structure will provide us some useful information about the long-time behavior of microorganism in random chemostat model. Finally, we make some comparison and analysis between both ways of modeling randomness and stochasticity in the chemostat model and show some numerical simulations to support our theoretical results. (c) 2021 Elsevier Ltd. All rights reserved.
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