多因素三维奇异摄动捕食-食饵模型的动力学分析

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-02-11 DOI:10.1002/mma.10803

Zhenlei Li, Yue Zhang

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引用次数: 0

摘要

本文讨论了具有恒定收获、避难效应和合作捕猎的三维奇异摄动捕食-食饵模型的动力学性质。系统在边界平衡和内部平衡处存在不同的分岔现象。对于三时间尺度系统，当折叠节点与普通奇点重合时产生小幅度振荡现象，当z $$ z $$为固定数值时，其子系统产生无头鸭式循环。然后考虑两个摄动参数的变化；系统产生类似于松弛振荡的振荡现象，随着摄动参数的变化，系统轨迹出现单循环、双循环和混沌。此外，我们还考虑了子系统的动态特性和随机因素对子系统的影响。

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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Dynamic Analysis of a Three-Dimensional Singular Perturbed Predator–Prey Model With Multiple Factors

In this paper, the dynamic properties of a three-dimensional singular perturbed predator–prey model with constant harvest, refuge effect, and cooperative hunt are discussed. The system has different bifurcation phenomena at the boundary equilibrium and the internal equilibrium. For the three-time scale system, the small amplitude oscillations phenomenon is produced when the folded node coincides with the ordinary singularity, and its subsystem produces canard cycle without head when we select $z$ as a fixed number. Then we consider the change of two perturbation parameters; the system produces an oscillation phenomenon similar to relaxation oscillation, and with the change of perturbation parameters, the system trajectory appears single cycle, double cycles, and chaos. In addition, we consider the dynamic properties of the subsystem and the influence of stochastic factors on the subsystem.

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.