Stability, bifurcation, and chaos control in a discrete predator-prey model with strong Allee effect

IF 1.8 3区 数学 Q1 MATHEMATICS
Ali Al Khabyah, Rizwan Ahmed, M. Akram, S. Akhtar
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引用次数: 4

Abstract

This work considers a discrete-time predator-prey system with a strong Allee effect. The existence and topological classification of the system's possible fixed points are investigated. Furthermore, the existence and direction of period-doubling and Neimark-Sacker bifurcations are explored at the interior fixed point using bifurcation theory and the center manifold theorem. A hybrid control method is used for controlling chaos and bifurcations. Some numerical examples are presented to verify our theoretical findings. Numerical simulations reveal that the discrete model has complex dynamics. Moreover, it is shown that the system with the Allee effect requires a much longer time to reach its interior fixed point.
具有强Allee效应的离散捕食-食饵模型的稳定性、分岔和混沌控制
本文考虑了一个具有强Allee效应的离散时间捕食者-猎物系统。研究了系统可能不动点的存在性和拓扑分类。进一步利用分岔理论和中心流形定理,探讨了内不动点上周期加倍分岔和neimmark - sacker分岔的存在性和方向。采用混合控制方法控制混沌和分岔。给出了一些数值算例来验证我们的理论结果。数值模拟结果表明,离散模型具有复杂的动力学特性。此外,研究还表明,有Allee效应的系统需要更长的时间才能到达其内部不动点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
AIMS Mathematics
AIMS Mathematics Mathematics-General Mathematics
CiteScore
3.40
自引率
13.60%
发文量
769
审稿时长
90 days
期刊介绍: AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.
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