Predator–prey systems with a variable habitat for predators in advective environments

IF 2.6 2区 数学 Q1 MATHEMATICS, APPLIED
Baifeng Zhang, Xianning Liu, Yangjiang Wei
{"title":"Predator–prey systems with a variable habitat for predators in advective environments","authors":"Baifeng Zhang,&nbsp;Xianning Liu,&nbsp;Yangjiang Wei","doi":"10.1111/sapm.12758","DOIUrl":null,"url":null,"abstract":"<p>Community composition in aquatic environments can be shaped by a broad array of factors, encompassing habitat conditions in addition to abiotic conditions and biotic interactions. This paper pertains to reaction–diffusion–advection predator–prey model featuring a variable predator habitat in advective environments, governed by a unidirectional flow. First, we establish the near-complete global dynamics of the system. In instances where the functional response to predation conforms to Holling-type I or II, we explore the uniqueness and stability of positive steady-state solutions via the application of particular auxiliary techniques, the comparison principle for parabolic equations, and perturbation analysis. Furthermore, we obtain the critical positions at the upper and lower boundaries of the predator's habitat, which determine the survival of the prey irrespective of the predator's growth rate. Finally, we show how the location and length of the predator's habitat affect the persistence and extinction of predators and prey in the event of a small population loss rate at the downstream end. From the biological point of view, these results contribute to our deeper understanding of the effects of habitat on aquatic populations and may have applications in aquaculture and the establishment of protection zones for aquatic species.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studies in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/sapm.12758","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

Abstract

Community composition in aquatic environments can be shaped by a broad array of factors, encompassing habitat conditions in addition to abiotic conditions and biotic interactions. This paper pertains to reaction–diffusion–advection predator–prey model featuring a variable predator habitat in advective environments, governed by a unidirectional flow. First, we establish the near-complete global dynamics of the system. In instances where the functional response to predation conforms to Holling-type I or II, we explore the uniqueness and stability of positive steady-state solutions via the application of particular auxiliary techniques, the comparison principle for parabolic equations, and perturbation analysis. Furthermore, we obtain the critical positions at the upper and lower boundaries of the predator's habitat, which determine the survival of the prey irrespective of the predator's growth rate. Finally, we show how the location and length of the predator's habitat affect the persistence and extinction of predators and prey in the event of a small population loss rate at the downstream end. From the biological point of view, these results contribute to our deeper understanding of the effects of habitat on aquatic populations and may have applications in aquaculture and the establishment of protection zones for aquatic species.

平流环境中捕食者栖息地可变的捕食者-猎物系统
水生环境中的群落组成可能受多种因素影响,除了非生物条件和生物相互作用外,还包括栖息地条件。本文涉及反应-扩散-对流捕食者-猎物模型,该模型以平流环境中可变的捕食者栖息地为特征,由单向流控制。首先,我们建立了该系统近乎完整的全局动力学。在捕食功能响应符合霍林类型 I 或 II 的情况下,我们通过应用特定的辅助技术、抛物方程的比较原理和扰动分析,探索正稳态解的唯一性和稳定性。此外,我们还得到了捕食者栖息地上下边界的临界位置,这些位置决定了猎物的存活率,而与捕食者的增长率无关。最后,我们展示了捕食者栖息地的位置和长度如何影响捕食者和猎物在下游小规模种群损失率情况下的存活和灭绝。从生物学角度来看,这些结果有助于我们深入理解栖息地对水生种群的影响,并可能在水产养殖和建立水生物种保护区方面有所应用。
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 求助全文
来源期刊
Studies in Applied Mathematics
Studies in Applied Mathematics 数学-应用数学
CiteScore
4.30
自引率
3.70%
发文量
66
审稿时长
>12 weeks
期刊介绍: Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信