Population dynamics in a Leslie-Gower predator-prey model with proportional prey refuge at low densities

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-24 DOI:10.1016/j.jmaa.2024.128993

Christian Cortés-García

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Abstract

In this paper we propose a mathematical Leslie-Gower predator-prey model, in which the prey takes refuge from the predator when its population size is below a critical threshold, the functional response of the predator is represented by a Holling II function, and the growth of the prey in the absence of the predator is subject to a semi-saturation parameter that affects its birth curve. Since the model is composed of two vector fields, its qualitative analysis includes, in addition to the determination of the number and stability of the equilibria for each vector field and belonging to the biological sense set, the study of the dynamics in the trajectories close to the dividing curve of the two vector fields in order to determine possible pseudo-equilibria. As a result, if the proposed model has a single inner equilibrium, then there is the possibility of having between one or at least two limit cycles, coexisting or not in both vector fields and around the inner equilibrium. Likewise, the model has a stable pseudo-equilibrium which may be surrounded by at least two limit cycle.

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莱斯利-高尔捕食者-猎物模型中的种群动态，低密度时猎物按比例避难

在本文中，我们提出了一个莱斯利-高尔捕食者-猎物数学模型，在该模型中，当猎物的种群数量低于临界阈值时，猎物会躲避捕食者，捕食者的功能响应由霍林 II 函数表示，而猎物在没有捕食者的情况下的生长受一个影响其出生曲线的半饱和参数的制约。由于该模型由两个矢量场组成，其定性分析除了确定每个矢量场的平衡点数量和稳定性以及属于生物意义集之外，还包括研究两个矢量场分界曲线附近轨迹的动态，以确定可能的伪平衡点。因此，如果所提出的模型有一个单一的内部平衡，那么在两个矢量场和内部平衡周围就有可能存在一个或至少两个极限循环。同样，该模型也有一个稳定的伪平衡，其周围可能存在至少两个极限循环。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.