分数Brown运动驱动的具有壁附着的恒化器模型的随机吸引子

doi:10.16088/j.issn.1001-6600.2022111903

摘要/Abstract

摘要： 大多数恒化器模型忽略了微生物的壁附着行为,并且对随机生物系统的记忆效应研究较少。基于此,本文研究由分数Brown运动驱动的具有壁附着的恒化器模型的随机吸引子的存在性。首先,引入合适的停时序列,将连续随机动力系统转化为一序列小区间上的离散随机动力系统;然后,在小的闭球内构造随机集,并证明其紧性、缓增性、吸引性,由此证明所生成随机动力系统拉回吸引子的存在性;最后,通过数值分析验证所得理论结果的正确性和有效性。

关键词: 随机吸引子, 分数Brown运动, 恒化器, 壁附着, 停时序列, 记忆效应

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

中图分类号: O175

李依洋, 曾才斌, 黄在堂. 分数Brown运动驱动的具有壁附着的恒化器模型的随机吸引子[J]. 广西师范大学学报（自然科学版）, 2023, 41(5): 61-68.

LI Yiyang, ZENG Caibin, HUANG Zaitang. Random Attractors for Chemostat Model with Wall Attachment Driven by Fractional Brownian Motion[J]. Journal of Guangxi Normal University(Natural Science Edition), 2023, 41(5): 61-68.

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