具有Caputo分数阶导数的离散捕食-捕食模型的复杂动力学与混沌控制

IF 1.7 4区工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Complexity Pub Date : 2025-02-21 DOI:10.1155/cplx/4415022

Rowshon Ara, Sohel Rana S. M.

{"title":"具有Caputo分数阶导数的离散捕食-捕食模型的复杂动力学与混沌控制","authors":"Rowshon Ara, Sohel Rana S. M.","doi":"10.1155/cplx/4415022","DOIUrl":null,"url":null,"abstract":"<div>\n <p>This work examines a discrete prey–predator model using the fractional derivative. The conditions for the existence and stability of the fixed points in the model are identified. The analysis is centered on exploring various bifurcations at the positive fixed point to understand their ecological implications. Using bifurcation theory, bifurcations related to period doubling, Neimark–Sacker, and strong resonances are studied. Lastly, the analytical results are confirmed through numerical simulations using the MATLAB package MatContM, and a controller is applied to relieve the extreme instability within the system.</p>\n </div>","PeriodicalId":50653,"journal":{"name":"Complexity","volume":"2025 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cplx/4415022","citationCount":"0","resultStr":"{\"title\":\"Complex Dynamics and Chaos Control of Discrete Prey–Predator Model With Caputo Fractional Derivative\",\"authors\":\"Rowshon Ara, Sohel Rana S. M.\",\"doi\":\"10.1155/cplx/4415022\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n <p>This work examines a discrete prey–predator model using the fractional derivative. The conditions for the existence and stability of the fixed points in the model are identified. The analysis is centered on exploring various bifurcations at the positive fixed point to understand their ecological implications. Using bifurcation theory, bifurcations related to period doubling, Neimark–Sacker, and strong resonances are studied. Lastly, the analytical results are confirmed through numerical simulations using the MATLAB package MatContM, and a controller is applied to relieve the extreme instability within the system.</p>\\n </div>\",\"PeriodicalId\":50653,\"journal\":{\"name\":\"Complexity\",\"volume\":\"2025 1\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2025-02-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1155/cplx/4415022\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Complexity\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1155/cplx/4415022\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Complexity","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1155/cplx/4415022","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

摘要

这项工作检查了一个离散的猎物-捕食者模型使用分数阶导数。确定了模型中不动点存在和稳定的条件。分析的重点是探索在正不动点上的各种分岔，以了解它们的生态含义。利用分岔理论，研究了与周期加倍、内马克-萨克和强共振有关的分岔。最后，利用MATLAB软件包MatContM对分析结果进行数值仿真验证，并采用控制器来缓解系统内部的极端不稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Complex Dynamics and Chaos Control of Discrete Prey–Predator Model With Caputo Fractional Derivative

查看原文本刊更多论文

Complex Dynamics and Chaos Control of Discrete Prey–Predator Model With Caputo Fractional Derivative

This work examines a discrete prey–predator model using the fractional derivative. The conditions for the existence and stability of the fixed points in the model are identified. The analysis is centered on exploring various bifurcations at the positive fixed point to understand their ecological implications. Using bifurcation theory, bifurcations related to period doubling, Neimark–Sacker, and strong resonances are studied. Lastly, the analytical results are confirmed through numerical simulations using the MATLAB package MatContM, and a controller is applied to relieve the extreme instability within the system.

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

Complexity 综合性期刊-数学跨学科应用

CiteScore

5.80

自引率

4.30%

发文量

595

审稿时长

>12 weeks

期刊介绍： Complexity is a cross-disciplinary journal focusing on the rapidly expanding science of complex adaptive systems. The purpose of the journal is to advance the science of complexity. Articles may deal with such methodological themes as chaos, genetic algorithms, cellular automata, neural networks, and evolutionary game theory. Papers treating applications in any area of natural science or human endeavor are welcome, and especially encouraged are papers integrating conceptual themes and applications that cross traditional disciplinary boundaries. Complexity is not meant to serve as a forum for speculation and vague analogies between words like “chaos,” “self-organization,” and “emergence” that are often used in completely different ways in science and in daily life.