Journal of Guangxi Normal University(Natural Science Edition) ›› 2023, Vol. 41 ›› Issue (5): 61-68.doi: 10.16088/j.issn.1001-6600.2022111903

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Random Attractors for Chemostat Model with Wall Attachment Driven by Fractional Brownian Motion

LI Yiyang1, ZENG Caibin1, HUANG Zaitang2*   

  1. 1. School of Mathematics, South China University of Technology, Guangzhou Guangdong 510640, China;
    2. School of Mathematics and Statistics, Nanning Normal University, Nanning Guangxi 530023, China
  • Received:2022-11-19 Revised:2023-01-19 Published:2023-10-09

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Abstract: Most chemostat models ignore the wall attachment of microorganisms and little seems to be known about the memory effect on stochastic biological systems. This paper is devoted to study the existence of random attractors for chemostat models with wall attachment driven by fractional Brownian motion. Firstly, a suitable stopping time sequence is established and the continuous random dynamical system is divided into discrete random dynamical systems on the small stopping time interval. Then the random set is constructed over a closed ball and its compactness, temperedness and attractivity are proved. Moreover, the required results on the existence of random attractor for generated random dynamical system are guaranteed. Finally, numerical simulations are carried out to verify the correctness and effectiveness of the theoretical results obtained.

Key words: random attractor, fractional Brownian motion, chemostat model, wall attachment, stopping time sequence, memory effect

CLC Number:  O175
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