STABILITY AND BIFURCATION OF A PREDATOR–PREY SYSTEM WITH MULTIPLE ANTI-PREDATOR BEHAVIORS

IF 1.3 4区数学 Q3 BIOLOGY

Journal of Biological Systems Pub Date : 2024-04-27 DOI:10.1142/s021833902450030x

YUE XIA, XINHAO HUANG, FENGDE CHEN, LIJUAN CHEN

引用次数: 0

Abstract

In this paper, a predator–prey system with multiple anti-predator behaviors is developed and studied, where not only the prey may spread between patches but also the fear effect and counter-attack behavior of the prey are taken into account. First, the stability and existence of coexistence equilibria are presented. The unique positive equilibrium may be a saddle-node or a cusp of codimension 2. Then, various transversality conditions of bifurcations such as saddle-node bifurcation, transcritical bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation are obtained. Moreover, compared with a single strategy, the multiple anti-predator strategies are more beneficial to the persistence and the population density of prey.

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具有多重反捕食者行为的捕食者-猎物系统的稳定性和分岔

本文建立并研究了一个具有多种反捕食行为的捕食者-猎物系统，其中不仅考虑了猎物可能在斑块间扩散，还考虑了猎物的恐惧效应和反击行为。首先介绍了共存均衡的稳定性和存在性。唯一的正平衡可能是一个鞍节点或一个标度为 2 的尖顶。然后，得到了鞍节点分岔、跨临界分岔、霍普夫分岔和波格丹诺夫-塔肯斯分岔等分岔的各种横向性条件。此外，与单一策略相比，多重反捕食者策略更有利于猎物的持续存在和种群密度。

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

Journal of Biological Systems 生物-生物学

CiteScore

2.80

自引率

12.50%

发文量

审稿时长

1 months

期刊介绍： The Journal of Biological Systems is published quarterly. The goal of the Journal is to promote interdisciplinary approaches in Biology and in Medicine, and the study of biological situations with a variety of tools, including mathematical and general systems methods. The Journal solicits original research papers and survey articles in areas that include (but are not limited to): Complex systems studies; isomorphies; nonlinear dynamics; entropy; mathematical tools and systems theories with applications in Biology and Medicine. Interdisciplinary approaches in Biology and Medicine; transfer of methods from one discipline to another; integration of biological levels, from atomic to molecular, macromolecular, cellular, and organic levels; animal biology; plant biology. Environmental studies; relationships between individuals, populations, communities and ecosystems; bioeconomics, management of renewable resources; hierarchy theory; integration of spatial and time scales. Evolutionary biology; co-evolutions; genetics and evolution; branching processes and phyllotaxis. Medical systems; physiology; cardiac modeling; computer models in Medicine; cancer research; epidemiology. Numerical simulations and computations; numerical study and analysis of biological data. Epistemology; history of science. The journal will also publish book reviews.