具有阿利效应的修正莱斯利-高尔食草动物模型在植物中的稳定性分析研究

Pankaj Kumar, Rupali Verma
{"title":"具有阿利效应的修正莱斯利-高尔食草动物模型在植物中的稳定性分析研究","authors":"Pankaj Kumar, Rupali Verma","doi":"10.37256/cm.5120242502","DOIUrl":null,"url":null,"abstract":"A modified Leslie-Gower plant-herbivore model is studied under the Allee effect. Holling-type II functional response is used to modify the model. Delay differential equations play an essential role in making this model more realistic and complicated. The non-trivial equilibrium E* (P* ≠ 0, H* ≠ 0) of the proposed model is calculated. Moreover, the stability and instability of the state variables, which include plant population P and herbivore population H are described graphically. It is shown that the system represents absolute stability when it has no time parameter (τ). When the time parameter is less than the threshold value, then the system exhibits asymptotic stability. In addition, the system surrenders its stability, and Hopf-bifurcation occurs when the time parameter surpasses the threshold value. The timeseries graphs are also represented. It is demonstrated that the system becomes more stable with the maximum rate of predation. MATLAB software is used to perform the graphs to justify the theoretical results.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Study of Stability Analysis of Modified Leslie-Gower Herbivore Model with Allee Effect in Plants\",\"authors\":\"Pankaj Kumar, Rupali Verma\",\"doi\":\"10.37256/cm.5120242502\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A modified Leslie-Gower plant-herbivore model is studied under the Allee effect. Holling-type II functional response is used to modify the model. Delay differential equations play an essential role in making this model more realistic and complicated. The non-trivial equilibrium E* (P* ≠ 0, H* ≠ 0) of the proposed model is calculated. Moreover, the stability and instability of the state variables, which include plant population P and herbivore population H are described graphically. It is shown that the system represents absolute stability when it has no time parameter (τ). When the time parameter is less than the threshold value, then the system exhibits asymptotic stability. In addition, the system surrenders its stability, and Hopf-bifurcation occurs when the time parameter surpasses the threshold value. The timeseries graphs are also represented. It is demonstrated that the system becomes more stable with the maximum rate of predation. MATLAB software is used to perform the graphs to justify the theoretical results.\",\"PeriodicalId\":504505,\"journal\":{\"name\":\"Contemporary Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Contemporary Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37256/cm.5120242502\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Contemporary Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37256/cm.5120242502","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

在阿利效应下,研究了一个修正的莱斯利-高尔植物-食草动物模型。霍林 II 型功能响应被用来修改该模型。延迟微分方程在使这一模型更加现实和复杂方面发挥了重要作用。计算了所提出模型的非三维平衡 E* (P*≠0,H*≠0)。此外,还用图形描述了包括植物种群 P 和食草动物种群 H 在内的状态变量的稳定性和不稳定性。结果表明,当系统没有时间参数(τ)时,它表示绝对稳定。当时间参数小于临界值时,系统表现出渐近稳定性。此外,当时间参数超过阈值时,系统将失去稳定性,出现霍普夫分岔。同时还表示了时间序列图。结果表明,随着捕食率的最大化,系统变得更加稳定。使用 MATLAB 软件绘制图表,以证明理论结果的正确性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Study of Stability Analysis of Modified Leslie-Gower Herbivore Model with Allee Effect in Plants
A modified Leslie-Gower plant-herbivore model is studied under the Allee effect. Holling-type II functional response is used to modify the model. Delay differential equations play an essential role in making this model more realistic and complicated. The non-trivial equilibrium E* (P* ≠ 0, H* ≠ 0) of the proposed model is calculated. Moreover, the stability and instability of the state variables, which include plant population P and herbivore population H are described graphically. It is shown that the system represents absolute stability when it has no time parameter (τ). When the time parameter is less than the threshold value, then the system exhibits asymptotic stability. In addition, the system surrenders its stability, and Hopf-bifurcation occurs when the time parameter surpasses the threshold value. The timeseries graphs are also represented. It is demonstrated that the system becomes more stable with the maximum rate of predation. MATLAB software is used to perform the graphs to justify the theoretical results.
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
自引率
0.00%
发文量
0
×
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