Journal
CHAOS SOLITONS & FRACTALS
Volume 165, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2022.112773
Keywords
Stochastic chemostat model; Time delay; Levy jumps; Extinction; Ergodic stationary distribution
Categories
Funding
- National Science and Technology Innovation 2030 of China Next-Generation Artificial Intelli-gence Major Project [2018AAA0101800]
- Graduate Scientific Research and Innovation Foundation of Chongqing, China [CYS22075]
- Key Project of Technological Innovation and Application Development Plan of Chongqing, China [cstc2020jscx-dxwtBX0044]
- National College Students' Innovation and Entrepreneurship Training Program, China [S202010619021, S202110619028]
- Application Basic Project of Sichuan Science and Technology Department, China [2017JY0336]
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This paper proposes a stochastic delayed chemostat model and discusses the existence and uniqueness of its global solution, as well as the threshold and optimal control conditions for the persistence and extinction of microorganisms. Numerical examples are provided to support the theoretical analysis, and the results show that stochastic noise and time delay play vital roles in controlling the persistence and extinction of microorganisms.
In this paper, a stochastic delayed chemostat model with nutrient storage and Levy jumps is proposed. Firstly, the existence and uniqueness of the positive global solution of the model are discussed. Then, the threshold (lambda) over bar. and optimal control conditions for the persistence in the mean and extinction of the microorganism x are obtained. Besides, the ergodic stationary distribution of the SDDE model under a low-level intensity of stochastic noise is deduced. Finally, some numerical examples are given to support the theoretical analysis results. The simulation results show that stochastic noise and time delay play a vital role in controlling the persistence and extinction of microorganisms, respectively. On the one hand, high-intensity noise can inhibit the growth of microorganisms. On the other hand, if tau > iota*, the corresponding deterministic model will become unstable and produce a Hopf bifurcation. Moreover, the solutions of the SDDE model will oscillate around the non-constant. F - periodic solution of the corresponding deterministic model.
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