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

IF 1.3 4区 数学 Q3 BIOLOGY
YUE XIA, XINHAO HUANG, FENGDE CHEN, LIJUAN CHEN
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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.

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
CiteScore
2.80
自引率
12.50%
发文量
31
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.
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