Global Dynamics of Two-Species Amensalism Model with Beddington–DeAngelis Functional Response and Fear Effect

IF 1.9 4区 数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Qun Zhu, Fengde Chen, Zhong Li, Lijuan Chen
{"title":"Global Dynamics of Two-Species Amensalism Model with Beddington–DeAngelis Functional Response and Fear Effect","authors":"Qun Zhu, Fengde Chen, Zhong Li, Lijuan Chen","doi":"10.1142/s0218127424500755","DOIUrl":null,"url":null,"abstract":"This paper investigates a two-species amensalism model that includes the fear effect on the first species and the Beddington–DeAngelis functional response. The existence and stability of possible equilibria are investigated. Under different parameters, there exist two stable equilibria which means that this model is not always globally asymptotically stable. Together with the existence of all possible equilibria and their stability, saddle connection and close orbits, we derive some conditions for transcritical bifurcation and saddle-node bifurcation. Furthermore, global dynamics analysis of the model is performed. It is observed that under certain parameter conditions, when the intensity of the fear effect is below a certain threshold value, as the fear effect increases it will only reduce the density of the first species population and will have no influence the extinction or existence of the first species population. However, when the fear effect exceeds this threshold, the increase of the fear effect will accelerate the extinction of the first species population. Finally, numerical simulations are performed to validate theoretical results.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Bifurcation and Chaos","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0218127424500755","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0

Abstract

This paper investigates a two-species amensalism model that includes the fear effect on the first species and the Beddington–DeAngelis functional response. The existence and stability of possible equilibria are investigated. Under different parameters, there exist two stable equilibria which means that this model is not always globally asymptotically stable. Together with the existence of all possible equilibria and their stability, saddle connection and close orbits, we derive some conditions for transcritical bifurcation and saddle-node bifurcation. Furthermore, global dynamics analysis of the model is performed. It is observed that under certain parameter conditions, when the intensity of the fear effect is below a certain threshold value, as the fear effect increases it will only reduce the density of the first species population and will have no influence the extinction or existence of the first species population. However, when the fear effect exceeds this threshold, the increase of the fear effect will accelerate the extinction of the first species population. Finally, numerical simulations are performed to validate theoretical results.
具有贝丁顿-德安吉利斯功能反应和恐惧效应的双物种同化模型的全局动力学特征
本文研究了一种双物种同调模型,其中包括对第一物种的恐惧效应和贝丁顿-德安吉利斯功能反应。本文研究了可能平衡的存在性和稳定性。在不同的参数下,存在两个稳定的平衡点,这意味着该模型并不总是全局渐近稳定的。结合所有可能平衡点的存在及其稳定性、鞍连接和近轨道,我们推导出了一些跨临界分岔和鞍节点分岔的条件。此外,我们还对模型进行了全局动力学分析。研究发现,在一定的参数条件下,当恐惧效应的强度低于某一临界值时,随着恐惧效应的增加,只会降低第一物种种群的密度,不会影响第一物种种群的灭绝或存在。然而,当恐惧效应超过这个临界值时,恐惧效应的增加将加速第一物种种群的灭绝。最后,我们进行了数值模拟来验证理论结果。
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
International Journal of Bifurcation and Chaos
International Journal of Bifurcation and Chaos 数学-数学跨学科应用
CiteScore
4.10
自引率
13.60%
发文量
237
审稿时长
2-4 weeks
期刊介绍: The International Journal of Bifurcation and Chaos is widely regarded as a leading journal in the exciting fields of chaos theory and nonlinear science. Represented by an international editorial board comprising top researchers from a wide variety of disciplines, it is setting high standards in scientific and production quality. The journal has been reputedly acclaimed by the scientific community around the world, and has featured many important papers by leading researchers from various areas of applied sciences and engineering. The discipline of chaos theory has created a universal paradigm, a scientific parlance, and a mathematical tool for grappling with complex dynamical phenomena. In every field of applied sciences (astronomy, atmospheric sciences, biology, chemistry, economics, geophysics, life and medical sciences, physics, social sciences, ecology, etc.) and engineering (aerospace, chemical, electronic, civil, computer, information, mechanical, software, telecommunication, etc.), the local and global manifestations of chaos and bifurcation have burst forth in an unprecedented universality, linking scientists heretofore unfamiliar with one another''s fields, and offering an opportunity to reshape our grasp of reality.
×
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