{"title":"Wave of chaos and Turing patterns in Rabbit–Lynx dynamics: Impact of fear and its carryover effects","authors":"Ranjit Kumar Upadhyay, Namrata Mani Tripathi, 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 , and 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.
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.