Wave of chaos and Turing patterns in Rabbit–Lynx dynamics: Impact of fear and its carryover effects

IF 3.4 2区 数学 Q1 MATHEMATICS, APPLIED Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-03-10 DOI:10.1016/j.cnsns.2025.108748
Ranjit Kumar Upadhyay, Namrata Mani Tripathi, Dipesh Barman
{"title":"Wave of chaos and Turing patterns in Rabbit–Lynx dynamics: Impact of fear and its carryover effects","authors":"Ranjit Kumar Upadhyay,&nbsp;Namrata Mani Tripathi,&nbsp;Dipesh Barman","doi":"10.1016/j.cnsns.2025.108748","DOIUrl":null,"url":null,"abstract":"<div><div>An attempt has been made to understand the joint impact of predator induced fear and its carryover consequences with diffusion. The prey population such as European rabbit is captured and consumed by the predator, Iberian lynx. In the absence of diffusion, the system undergoes saddle–node and Hopf-bifurcation with respect to the carryover and fear parameters. Both the fear and carryover parameter affect the system dynamics in a contradictory manner, i.e., higher amount of fear level destabilizes the system dynamics whereas higher amount of carryover level stabilizes it. Additionally, the creation and destruction of interior equilibrium points have been observed under the variation of both these parameters independently. Furthermore, the temporal system undergoes Cusp bifurcation in two parametric plane such as <span><math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>, <span><math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>−</mo><mi>δ</mi></mrow></math></span> and <span><math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>−</mo><mi>δ</mi></mrow></math></span> plane. The global stability of the temporal system has been analyzed both analytically and numerically. However, in the presence of diffusion, the system experiences Turing instability. Numerical simulation shows the occurrence of spatio-temporal pattern formation for the proposed system. Further, it exhibits wave of chaos phenomenon for lower level of fear and carryover parameter value which is very important phenomenon to understand the spread of disease dynamics. Furthermore, the effect of the predator induced fear on the system dynamics has been explored in non-local sense for the spatio-temporal system. Our research integrates the model dynamics with its analysis by a variety of figures and diagrams that visually represent and reinforce our results. By examining non-linear models, we reveal unique and noteworthy patterns that offer fresh perspectives. These discoveries are particularly useful for biologists aiming to deepen their understanding of eco-epidemiological system dynamics in a practical context. The graphical depictions throughout our study play a key role in delivering a thorough analysis, making the findings more approachable and relevant to both researchers and field practitioners.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"145 ","pages":"Article 108748"},"PeriodicalIF":3.4000,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570425001595","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

An attempt has been made to understand the joint impact of predator induced fear and its carryover consequences with diffusion. The prey population such as European rabbit is captured and consumed by the predator, Iberian lynx. In the absence of diffusion, the system undergoes saddle–node and Hopf-bifurcation with respect to the carryover and fear parameters. Both the fear and carryover parameter affect the system dynamics in a contradictory manner, i.e., higher amount of fear level destabilizes the system dynamics whereas higher amount of carryover level stabilizes it. Additionally, the creation and destruction of interior equilibrium points have been observed under the variation of both these parameters independently. Furthermore, the temporal system undergoes Cusp bifurcation in two parametric plane such as f1f2, f1δ and f2δ plane. The global stability of the temporal system has been analyzed both analytically and numerically. However, in the presence of diffusion, the system experiences Turing instability. Numerical simulation shows the occurrence of spatio-temporal pattern formation for the proposed system. Further, it exhibits wave of chaos phenomenon for lower level of fear and carryover parameter value which is very important phenomenon to understand the spread of disease dynamics. Furthermore, the effect of the predator induced fear on the system dynamics has been explored in non-local sense for the spatio-temporal system. Our research integrates the model dynamics with its analysis by a variety of figures and diagrams that visually represent and reinforce our results. By examining non-linear models, we reveal unique and noteworthy patterns that offer fresh perspectives. These discoveries are particularly useful for biologists aiming to deepen their understanding of eco-epidemiological system dynamics in a practical context. The graphical depictions throughout our study play a key role in delivering a thorough analysis, making the findings more approachable and relevant to both researchers and field practitioners.
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
求助全文
约1分钟内获得全文 去求助
来源期刊
Communications in Nonlinear Science and Numerical Simulation
Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
CiteScore
6.80
自引率
7.70%
发文量
378
审稿时长
78 days
期刊介绍: The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.
期刊最新文献
Nonconforming finite element method for a 4th-order history-dependent hemivariational inequality Synchronization in predefined time of octonion-valued competitive neural networks: Aperiodic complete intermittent control and non-separation method Wave of chaos and Turing patterns in Rabbit–Lynx dynamics: Impact of fear and its carryover effects Modeling and simulation of the conserved N-component Allen–Cahn model on evolving surfaces Editorial Board
×
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