{"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}
引用次数: 0
Abstract
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.
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.
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