具有和不具有Allee效应的双斑块种群模型的稳态动力学

IF 0.4 Q4 MATHEMATICS, APPLIED Mathematics in applied sciences and engineering Pub Date : 2023-09-22 DOI:10.5206/mase/16474
Laurence Ketchemen Tchouaga, Frithjof Lutscher
{"title":"具有和不具有Allee效应的双斑块种群模型的稳态动力学","authors":"Laurence Ketchemen Tchouaga, Frithjof Lutscher","doi":"10.5206/mase/16474","DOIUrl":null,"url":null,"abstract":"Most biological populations reside in landscapes that consist of many different patches of different quality. Different species differ in their movement behavior, habitat preference and growth rates. Historically, mathematical models for population dynamics have made many simplifying assumptions, such as a single patch or homogeneous landscapes. Recent models have begun to implement landscape heterogeneity and individual movement characteristics, but many of those are based on logistic growth and linear analysis of the zero state. We consider a two-patch model with more general growth functions that can include Allee effects. We prove the existence of steady states and classify their qualitative behavior. In some special cases, we explicitly calculate their stability and use these results to give conditions for when the system exhibits bistability, i.e., the coexistence of locally stable states. We also study bifurcations with respect to the size of habitat patches and give conditions for forward and backward bifurcations.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"29 1","pages":"0"},"PeriodicalIF":0.4000,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Steady-state dynamics in a two-patch population model with and without Allee effect\",\"authors\":\"Laurence Ketchemen Tchouaga, Frithjof Lutscher\",\"doi\":\"10.5206/mase/16474\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Most biological populations reside in landscapes that consist of many different patches of different quality. Different species differ in their movement behavior, habitat preference and growth rates. Historically, mathematical models for population dynamics have made many simplifying assumptions, such as a single patch or homogeneous landscapes. Recent models have begun to implement landscape heterogeneity and individual movement characteristics, but many of those are based on logistic growth and linear analysis of the zero state. We consider a two-patch model with more general growth functions that can include Allee effects. We prove the existence of steady states and classify their qualitative behavior. In some special cases, we explicitly calculate their stability and use these results to give conditions for when the system exhibits bistability, i.e., the coexistence of locally stable states. We also study bifurcations with respect to the size of habitat patches and give conditions for forward and backward bifurcations.\",\"PeriodicalId\":93797,\"journal\":{\"name\":\"Mathematics in applied sciences and engineering\",\"volume\":\"29 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-09-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics in applied sciences and engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5206/mase/16474\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics in applied sciences and engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5206/mase/16474","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

摘要

大多数生物种群居住在由许多不同质量的不同斑块组成的景观中。不同的物种在运动行为、栖息地偏好和生长速度上存在差异。历史上,人口动态的数学模型做出了许多简化的假设,例如单一斑块或均匀景观。最近的模型已经开始实现景观异质性和个体运动特征,但其中许多是基于逻辑增长和零状态的线性分析。我们考虑一个具有更一般的生长函数的双补丁模型,可以包括Allee效应。证明了稳态的存在性,并对其定性行为进行了分类。在一些特殊情况下,我们显式地计算了它们的稳定性,并利用这些结果给出了系统呈现双稳定性的条件,即局部稳定状态的共存。我们还研究了与生境斑块大小有关的分岔,并给出了向前和向后分岔的条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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
Steady-state dynamics in a two-patch population model with and without Allee effect
Most biological populations reside in landscapes that consist of many different patches of different quality. Different species differ in their movement behavior, habitat preference and growth rates. Historically, mathematical models for population dynamics have made many simplifying assumptions, such as a single patch or homogeneous landscapes. Recent models have begun to implement landscape heterogeneity and individual movement characteristics, but many of those are based on logistic growth and linear analysis of the zero state. We consider a two-patch model with more general growth functions that can include Allee effects. We prove the existence of steady states and classify their qualitative behavior. In some special cases, we explicitly calculate their stability and use these results to give conditions for when the system exhibits bistability, i.e., the coexistence of locally stable states. We also study bifurcations with respect to the size of habitat patches and give conditions for forward and backward bifurcations.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
1.40
自引率
0.00%
发文量
0
审稿时长
21 weeks
期刊最新文献
Solution of fractional modified Kawahara equation: a semi-analytic approach Recovery of an initial temperature of a one-dimensional body from finite time-observations Multiscale modeling approach to assess the impact of antibiotic treatment for COVID-19 on MRSA transmission and alternative immunotherapy treatment options The minimal invasion speed of two competing species in homogeneous environment Assessing the impact of host predation with Holling II response on the transmission of Chagas disease
×
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