A Reaction-Diffusion-Advection Chemostat Model in a Flowing Habitat: Mathematical Analysis and Numerical Simulations

Wang Zhang, Hua Nie, Jianhua Wu
{"title":"A Reaction-Diffusion-Advection Chemostat Model in a Flowing Habitat: Mathematical Analysis and Numerical Simulations","authors":"Wang Zhang, Hua Nie, Jianhua Wu","doi":"10.1142/s0218127423500736","DOIUrl":null,"url":null,"abstract":"This paper is concerned with a reaction–diffusion–advection chemostat model with two species growing and competing for a single-limited resource. By taking the growth rates of the two species as variable parameters, we study the effect of growth rates on the dynamics of this system. It is found that there exist several critical curves, which may classify the dynamics of this system into three scenarios: (1) extinction of both species; (2) competitive exclusion; (3) coexistence. Moreover, we take numerical approaches to further understand the potential behaviors of the above critical curves and observe that the bistable phenomenon can occur, besides competitive exclusion and coexistence. To further study the effect of advection and diffusion on the dynamics of this system, we present the bifurcation diagrams of positive equilibrium solutions of the single species model and the two-species model with the advection rates and the diffusion rates increasing, respectively. These numerical results indicate that advection and diffusion play a key role in determining the dynamics of two species competing in a flow reactor.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":"47 1","pages":"2350073:1-2350073:29"},"PeriodicalIF":0.0000,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Bifurc. Chaos","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218127423500736","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1

Abstract

This paper is concerned with a reaction–diffusion–advection chemostat model with two species growing and competing for a single-limited resource. By taking the growth rates of the two species as variable parameters, we study the effect of growth rates on the dynamics of this system. It is found that there exist several critical curves, which may classify the dynamics of this system into three scenarios: (1) extinction of both species; (2) competitive exclusion; (3) coexistence. Moreover, we take numerical approaches to further understand the potential behaviors of the above critical curves and observe that the bistable phenomenon can occur, besides competitive exclusion and coexistence. To further study the effect of advection and diffusion on the dynamics of this system, we present the bifurcation diagrams of positive equilibrium solutions of the single species model and the two-species model with the advection rates and the diffusion rates increasing, respectively. These numerical results indicate that advection and diffusion play a key role in determining the dynamics of two species competing in a flow reactor.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
流动生境中的反应-扩散-平流变化学模型:数学分析与数值模拟
本文研究了两种生物生长并竞争单一有限资源的反应-扩散-平流趋化模型。以两种植物的生长速率为可变参数,研究了生长速率对系统动力学的影响。研究发现,存在几个临界曲线,可以将该系统的动力学分为三种情景:(1)两个物种都灭绝;(二)竞争性排斥;(3)共存。此外,我们采用数值方法进一步了解上述临界曲线的潜在行为,并观察到除了竞争排斥和共存之外,还可能出现双稳态现象。为了进一步研究平流和扩散对系统动力学的影响,我们分别给出了随平流速率和扩散速率增加的单种模型和两种模型的正平衡解的分岔图。这些数值结果表明,平流和扩散在决定流动反应器中两种物质竞争的动力学中起着关键作用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
Global Analysis of Riccati Quadratic Differential Systems Bifurcation and Spatiotemporal Patterns of SI Epidemic Model with Diffusion Approximate Equivalence of Higher-Order Feedback and Its Application in Chaotic Systems Four Novel Dual Discrete Memristor-Coupled Hyperchaotic Maps A Hierarchical Multiscenario H.265/HEVC Video Encryption Scheme
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1