具有猎物避难所和Allee效应的捕食者-食饵模型的动态复杂性

IF 0.8 4区数学 Q2 MATHEMATICS

Turkish Journal of Mathematics Pub Date : 2023-11-09 DOI:10.55730/1300-0098.3481

JIANPING GAO, JIANGHONG ZHANG, WENYAN LIAN

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引用次数: 0

摘要

我们考虑了一个具有非单调功能响应的捕食者-猎物模型，该模型包括一个猎物避难所和对猎物的强Allee效应。研究了内部平衡态的多重存在性和稳定性。分岔分析表明，该模型可以表现出多种分岔(如鞍节点分岔、Hopf-Andronov分岔和Bogdanov-Takens分岔)。结果表明，该模型存在多种参数值，在这些参数值下，模型表现出一个极限环，一个同斜轨道，甚至许多异斜曲线。结果表明，模型中的猎物庇护所带来了丰富的动态特性，使系统对参数值更加敏感。本工作的主要目的是提供一个完整的数学分析，避难所带来的影响。

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Dynamical complexity of a predator-prey model with a prey refuge and Allee effect

We consider a predator-prey model with a non-monotonic functional response encompassing a prey refuge and a strong Allee effect on the prey. The multiple existence and stability of interior equilibria are investigated. The bifurcation analysis shows this model can exhibit numerous kinds of bifurcations (e.g., saddle-node, Hopf-Andronov and Bogdanov-Takens bifurcations). It is found that there exist diverse parameter values for which the model exhibits a limit cycle, a homoclinic orbit, and even many heteroclinic curves. The results obtained reveal the prey refuge in the model brings rich dynamics and makes the system more sensitive to parameter values. The main purpose of the present work is to offer a complete mathematical analysis of the effect that the refuge brings about.

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来源期刊

Turkish Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

10.00%

发文量

161

审稿时长

6-12 weeks

期刊介绍： The Turkish Journal of Mathematics is published electronically 6 times a year by the Scientific and Technological Research Council of Turkey (TÜBİTAK) and accepts English-language original research manuscripts in the field of mathematics. Contribution is open to researchers of all nationalities.