具有备选猎物的离散捕食者-猎物模型的分岔和稳定性分析

IF 1.9 3区数学 Q1 MATHEMATICS

Qualitative Theory of Dynamical Systems Pub Date : 2024-07-05 DOI:10.1007/s12346-024-01092-y

Ceyu Lei, Xiaoling Han, Weiming Wang

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引用次数: 0

摘要

本文研究了一类具有替代猎物的离散捕食者-猎物模型的动力学。我们证明了解的有界性、模型平衡点的存在性和局部/全局稳定性，并验证了翻转分岔和 Neimark-Sacker 分岔的存在性。此外，我们还利用最大李雅普诺夫指数和等周图验证了一类捕食者-猎物模型的双参数空间中存在周期性结构，即阿诺德舌和虾形结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Bifurcation and Stability Analysis of a Discrete Predator–Prey Model with Alternative Prey

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Bifurcation and Stability Analysis of a Discrete Predator–Prey Model with Alternative Prey

In this paper, we investigate the dynamics of a class of discrete predator–prey model with alternative prey. We prove the boundedness of the solution, the existence and local/global stability of equilibrium points of the model, and verify the existence of flip bifurcation and Neimark-Sacker bifurcation. In addition, we use the maximum Lyapunov exponent and isoperimetric diagrams to verify the existence of periodic structures namely Arnold tongue and the shrimp-shaped structures in bi-parameter spaces of a class of predator–prey model.

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来源期刊

Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

14.30%

发文量

130

期刊介绍： Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.