非自治单种群Chemostat模型的全局渐近稳定性
Global Asymptotic Stability of a Non-Autonomous Single-Population Chemostat Model
DOI: 10.12677/AAM.2021.104128, PDF,    科研立项经费支持
作者: 邢喜民, 薛婷婷, 徐加波*：新疆工程学院，数理学院，新疆 乌鲁木齐；辛 巧：伊犁师范大学，数学与统计分院，新疆 伊宁
关键词: 种群动力系统；Chemostat模型；非自治系统；全局渐近稳定；Population Dynamic System； Chemostat Model； Non-Autonomous Systems； Globally Asymptotically Stable
摘要: 本文首先考察了营养稀释率与移除率相同情形下的非自治单种群Chemostat系统的动力学行为。其次，假定营养稀释率与移除率相同，降低了微分方程的维数。最后，利用常微分方程的比较原理，给出了Chemostat系统稳定性的充分条件。
Abstract: In this paper, the dynamic behavior of a non-autonomous single-population Chemostat system with the same nutrient dilution rate and removal rate is investigated. Then, under the assumption that the nutrient dilution rate and removal rate are the same, the dimension of the differential equation is reduced. Finally, by using the comparison principle of ordinary differential equations, the sufficient conditions for the stability of Chemostat system are given.
文章引用：邢喜民, 辛巧, 薛婷婷, 徐加波. 非自治单种群Chemostat模型的全局渐近稳定性[J]. 应用数学进展, 2021, 10(4): 1184-1190. https://doi.org/10.12677/AAM.2021.104128

参考文献

[1] 孙明娟, 董庆来, 代丽. 一类带有毒素生产的比率型Chemostat模型的定性分析[J]. 系统科学与数学, 2017, 37(9): 20-27.
[2] 董庆来, 马万彪. 具有时滞和可变营养消耗率的比率型Chemostat模型稳定性分析[J]. 系统科学与数学, 2009, 29(2): 86-99.
[3] 周玉平, 黄迅成. 一个三维Chemostat竞争系统的Hopf分支和周期解[J]. 应用数学, 2006, 19(2): 178-184.
[4] 宋国华, 李秀琴, 窦家维, 贺庆棠. Chemostat系统中Hopf分支的存在性[J]. 系统科学与数学, 2001, 21(4): 486-490.
[5] Wang, L., Jiang, D. and Wolkowicz, G.S.K. (2019) Global Asymptotic Behavior of a Multi-Species Stochastic Chemostat Model with Discrete Delays. Journal of Dynamics and Differential Equations, 32, 849-872. [Google Scholar] [CrossRef] 
[6] Pu, W.J., Jiang, D., Wang, Y., et al. (2019) Spatial Dynamics of a Nonlocal Delayed Unstirred Chemostat Model with Periodic Input. International Journal of Biomathematics, 12, Article ID: 1950065. [Google Scholar] [CrossRef] 
[7] Zhang, X. and Yuan, R. (2019) The Existence of Stationary Distribution of a Stochastic Delayed Chemostat Model. Applied Mathematics Letters, 93, 15-21. [Google Scholar] [CrossRef] 
[8] Gao, M., Jiang, D. and Hayat, T. (2019) Stationary Distribution and Periodic Solution of Stochastic Chemostat Models with Single-Species Growth on Two Nutrients. International Journal of Biomathematics, 12, Article ID: 1950063. [Google Scholar] [CrossRef] 
[9] Feng, X., Sun, S., Zhang, T., et al. (2018) The Effect of Parameters on Positive Solutions and Asymptotic Behavior of an Unstirred Chemostat Model with B-D Functional Response. Advances in Difference Equations, 2018, Article Number: 181. [Google Scholar] [CrossRef] 
[10] Gong, C., Xu, C. and Yuan, S. (2017) Threshold of a Stochastic Chemostat Model with the Ivlev Functional Response Function. Journal of University of Shanghai for Science & Technology, 39, 1-6.
[11] Wang, L. and Jiang, D. (2017) Asymptotic Properties of a Stochastic Chemostat Including Species Death Rate. Mathematical Methods in the Applied Sciences, 41, 438-456. [Google Scholar] [CrossRef] 
[12] Wang, L. and Jiang, D. (2017) Periodic Solution for the Stochastic Chemostat with General Response Function. Physica A: Statistical Mechanics and Its Applications, 486, 378-385. [Google Scholar] [CrossRef] 
[13] Sun, S., Guo, C. and Liu, X. (2018) Hopf Bifurcation of a Delayed Chemostat Model with General Monotone Response Functions. Computational and Applied Mathematics, 37, 2714-2737.
[14] Sun, S., Sun, Y., Zhang, G., et al. (2017) Dynamical Behavior of a Stochastic Two-Species Monod Competition Chemostat Model. Applied Mathematics and Computation, 298, 153-170. [Google Scholar] [CrossRef] 

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