Bifurcation Analysis of a Predator–Prey Model with Alternative Prey and Prey Refuges

IF 1.9 4区数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

International Journal of Bifurcation and Chaos Pub Date : 2024-03-12 DOI:10.1142/s0218127424500214

Wenzhe Cui, Yulin Zhao

引用次数: 0

Abstract

In this paper, we study the codimensions of Hopf bifurcation and Bogdanov–Takens bifurcation of a predator–prey model with alternative prey and prey refuges, which was proposed by Chen et al. [2023]. The results show that the predator–prey model can undergo a supercritical Hopf bifurcation or a Bogdanov–Takens bifurcation of codimension two under certain parameter conditions. It means that there are some predator–prey models with an alternative prey and prey refuges which have a limit cycle or a homoclinic loop. Moreover, it is also shown that the codimension of Hopf bifurcation is at most one and codimension of Bogdanov–Takens bifurcation is at most two.

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具有备选猎物和猎物庇护所的捕食者-猎物模型的分岔分析

本文研究了Chen等[2023]提出的具有替代性猎物和猎物避难所的捕食者-猎物模型的霍普夫分岔和波格丹诺夫-塔肯斯分岔的标度。结果表明，在一定的参数条件下，捕食者-猎物模型会发生超临界霍普夫分岔或标度为二的波格丹诺夫-塔肯斯分岔。这意味着存在一些具有替代性猎物和猎物避难所的捕食者-猎物模型，它们会出现极限循环或同次循环。此外，还证明了霍普夫分岔的标度最多为一，而波格丹诺夫-塔肯斯分岔的标度最多为二。

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

International Journal of Bifurcation and Chaos 数学-数学跨学科应用

CiteScore

4.10

自引率

13.60%

发文量

237

审稿时长

2-4 weeks

期刊介绍： The International Journal of Bifurcation and Chaos is widely regarded as a leading journal in the exciting fields of chaos theory and nonlinear science. Represented by an international editorial board comprising top researchers from a wide variety of disciplines, it is setting high standards in scientific and production quality. The journal has been reputedly acclaimed by the scientific community around the world, and has featured many important papers by leading researchers from various areas of applied sciences and engineering. The discipline of chaos theory has created a universal paradigm, a scientific parlance, and a mathematical tool for grappling with complex dynamical phenomena. In every field of applied sciences (astronomy, atmospheric sciences, biology, chemistry, economics, geophysics, life and medical sciences, physics, social sciences, ecology, etc.) and engineering (aerospace, chemical, electronic, civil, computer, information, mechanical, software, telecommunication, etc.), the local and global manifestations of chaos and bifurcation have burst forth in an unprecedented universality, linking scientists heretofore unfamiliar with one another''s fields, and offering an opportunity to reshape our grasp of reality.