{"title":"A Nonlocal Reaction-Diffusion-Advection System Modeling the Phytoplankton and Zooplankton","authors":"Biao Wang, Hua Nie, Jianhua Wu","doi":"10.1111/sapm.12785","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>We present a nonlocal reaction-diffusion-advection system that models the predator–prey relationship between zooplankton and phytoplankton species in a eutrophic vertical water column. The invasion dynamics of zooplankton are analyzed in terms of the spontaneous death rates and buoyant/sinking velocities of both phytoplankton and zooplankton. Our analysis reveals that the zooplankton species can successfully invade and coexist with the phytoplankton only under conditions of low spontaneous death rates and matching buoyant/sinking velocities with phytoplankton. Additionally, we derived asymptotic profiles for the unique positive steady state of this system when one of the sinking or buoyant velocities of either phytoplankton or zooplankton approaches infinity, while the other velocity remains fixed. These findings highlight the significant role of advection due to buoyancy in shaping the dynamics of plankton ecosystems.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2024-11-15","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.12785","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
We present a nonlocal reaction-diffusion-advection system that models the predator–prey relationship between zooplankton and phytoplankton species in a eutrophic vertical water column. The invasion dynamics of zooplankton are analyzed in terms of the spontaneous death rates and buoyant/sinking velocities of both phytoplankton and zooplankton. Our analysis reveals that the zooplankton species can successfully invade and coexist with the phytoplankton only under conditions of low spontaneous death rates and matching buoyant/sinking velocities with phytoplankton. Additionally, we derived asymptotic profiles for the unique positive steady state of this system when one of the sinking or buoyant velocities of either phytoplankton or zooplankton approaches infinity, while the other velocity remains fixed. These findings highlight the significant role of advection due to buoyancy in shaping the dynamics of plankton ecosystems.
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.
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