在清晰、模糊和空间环境中,死亡率对捕食者-猎物模型的影响:一种动态方法

IF 5.3 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Chaos Solitons & Fractals Pub Date : 2025-01-22 DOI:10.1016/j.chaos.2025.116017
Shivam, Teekam Singh, Shivam Rawat, Anupam Singh
{"title":"在清晰、模糊和空间环境中,死亡率对捕食者-猎物模型的影响:一种动态方法","authors":"Shivam, Teekam Singh, Shivam Rawat, Anupam Singh","doi":"10.1016/j.chaos.2025.116017","DOIUrl":null,"url":null,"abstract":"The dynamic relationship between predators and prey plays a vital role in upholding equilibrium within the natural environment. Mortality plays a crucial role in maintaining the delicate equilibrium of ecosystems. This paper delves into the consequences of mortality in a predator–prey model that incorporates hydra, the Allee effect, and mutual interference among predators. We first established a crisp predator–prey model and then transformed it into a fuzzy model, representing the control parameters as triangular intuitionistic fuzzy numbers. We transform the fuzzy model into the defuzzified model by applying a graded mean integration technique. This technique allows for efficient solution determination using triangular intuitionistic fuzzy numbers. The theoretical section explores the presence and durability of equilibrium points and Hopf bifurcation on mortality parameters. Living organisms have the ability to move from one place to another, so we created a spatial model based on a crisp model. In order to investigate the impact of random movement of species within a population in an isolated area with different mortality parameters, we employ Turing instability. We confirm the theoretical results using the MATLAB package. The phase trajectories for various initial conditions in both environments are displayed, showcasing the species’ population fluctuations. We use the MATCONT package to illustrate the various scenarios that emerge when we alter the mortality parameters. We calculate the presence of saddle–node (SN), Hopf point (H), and Cusp point (CS) in the model. In addition, our spatial model analysis reveals various spatial structures within the isolated domain, including spots, stripes, and mixed patterns. The results indicate that mortality has a beneficial impact on the prey–predator population, helping to sustain ecological balance.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"74 1","pages":""},"PeriodicalIF":5.3000,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Effects of mortality on a predator–prey model in crisp, fuzzy, and spatial environments: A dynamical approach\",\"authors\":\"Shivam, Teekam Singh, Shivam Rawat, Anupam Singh\",\"doi\":\"10.1016/j.chaos.2025.116017\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The dynamic relationship between predators and prey plays a vital role in upholding equilibrium within the natural environment. Mortality plays a crucial role in maintaining the delicate equilibrium of ecosystems. This paper delves into the consequences of mortality in a predator–prey model that incorporates hydra, the Allee effect, and mutual interference among predators. We first established a crisp predator–prey model and then transformed it into a fuzzy model, representing the control parameters as triangular intuitionistic fuzzy numbers. We transform the fuzzy model into the defuzzified model by applying a graded mean integration technique. This technique allows for efficient solution determination using triangular intuitionistic fuzzy numbers. The theoretical section explores the presence and durability of equilibrium points and Hopf bifurcation on mortality parameters. Living organisms have the ability to move from one place to another, so we created a spatial model based on a crisp model. In order to investigate the impact of random movement of species within a population in an isolated area with different mortality parameters, we employ Turing instability. We confirm the theoretical results using the MATLAB package. The phase trajectories for various initial conditions in both environments are displayed, showcasing the species’ population fluctuations. We use the MATCONT package to illustrate the various scenarios that emerge when we alter the mortality parameters. We calculate the presence of saddle–node (SN), Hopf point (H), and Cusp point (CS) in the model. In addition, our spatial model analysis reveals various spatial structures within the isolated domain, including spots, stripes, and mixed patterns. The results indicate that mortality has a beneficial impact on the prey–predator population, helping to sustain ecological balance.\",\"PeriodicalId\":9764,\"journal\":{\"name\":\"Chaos Solitons & Fractals\",\"volume\":\"74 1\",\"pages\":\"\"},\"PeriodicalIF\":5.3000,\"publicationDate\":\"2025-01-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Chaos Solitons & Fractals\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1016/j.chaos.2025.116017\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos Solitons & Fractals","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1016/j.chaos.2025.116017","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0

摘要

捕食者和猎物之间的动态关系在维持自然环境中的平衡中起着至关重要的作用。死亡率在维持生态系统的微妙平衡方面起着至关重要的作用。本文探讨了在一个包含水螅、Allee效应和捕食者相互干扰的捕食者-被捕食者模型中死亡率的后果。我们首先建立了一个清晰的捕食者-猎物模型,然后将其转化为一个模糊模型,将控制参数表示为三角直觉模糊数。采用梯度均值积分技术将模糊模型转化为去模糊化模型。这种技术允许使用三角直觉模糊数进行有效的解确定。理论部分探讨了平衡点和Hopf分岔在死亡率参数上的存在性和持久性。生物体有从一个地方移动到另一个地方的能力,所以我们基于一个清晰的模型创建了一个空间模型。为了研究具有不同死亡率参数的孤立区域内种群内物种随机迁移的影响,我们采用了图灵不稳定性。利用MATLAB软件包对理论结果进行了验证。显示了两种环境中不同初始条件的相位轨迹,展示了物种的种群波动。我们使用MATCONT包来说明当我们改变死亡率参数时出现的各种情况。我们计算了模型中鞍节点(SN)、Hopf点(H)和Cusp点(CS)的存在。此外,我们的空间模型分析揭示了孤立域中的各种空间结构,包括斑点,条纹和混合模式。结果表明,死亡对捕食者种群数量有有益影响,有助于维持生态平衡。
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
Effects of mortality on a predator–prey model in crisp, fuzzy, and spatial environments: A dynamical approach
The dynamic relationship between predators and prey plays a vital role in upholding equilibrium within the natural environment. Mortality plays a crucial role in maintaining the delicate equilibrium of ecosystems. This paper delves into the consequences of mortality in a predator–prey model that incorporates hydra, the Allee effect, and mutual interference among predators. We first established a crisp predator–prey model and then transformed it into a fuzzy model, representing the control parameters as triangular intuitionistic fuzzy numbers. We transform the fuzzy model into the defuzzified model by applying a graded mean integration technique. This technique allows for efficient solution determination using triangular intuitionistic fuzzy numbers. The theoretical section explores the presence and durability of equilibrium points and Hopf bifurcation on mortality parameters. Living organisms have the ability to move from one place to another, so we created a spatial model based on a crisp model. In order to investigate the impact of random movement of species within a population in an isolated area with different mortality parameters, we employ Turing instability. We confirm the theoretical results using the MATLAB package. The phase trajectories for various initial conditions in both environments are displayed, showcasing the species’ population fluctuations. We use the MATCONT package to illustrate the various scenarios that emerge when we alter the mortality parameters. We calculate the presence of saddle–node (SN), Hopf point (H), and Cusp point (CS) in the model. In addition, our spatial model analysis reveals various spatial structures within the isolated domain, including spots, stripes, and mixed patterns. The results indicate that mortality has a beneficial impact on the prey–predator population, helping to sustain ecological balance.
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
Chaos Solitons & Fractals
Chaos Solitons & Fractals 物理-数学跨学科应用
CiteScore
13.20
自引率
10.30%
发文量
1087
审稿时长
9 months
期刊介绍: Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.
期刊最新文献
Vibration reduction research of a thin beam system by employing distributed coupling nonlinear energy sinks Rheostatic effect of a magnetic field on the onset of chaotic and periodic motions in a five-dimensional magnetoconvective Lorenz system Nonreciprocal cavity magnonics system for amplification of photonic spin Hall effect Gradient based optimization of Chaogates A novel Riemann–Hilbert formulation-based reduction method to an integrable reverse-space nonlocal Manakov equation and its applications
×
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