Dynamic Analysis of a Ratio-Dependent Food Chain Model with Prey-Taxis

IF 1.9 4区数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

International Journal of Bifurcation and Chaos Pub Date : 2024-03-09 DOI:10.1142/s0218127424500378

Zhuzhen Liao, Cui Song, Zhi-Cheng Wang

引用次数: 0

Abstract

In this paper, we consider a food chain model with ratio-dependent functional response and prey-taxis. We first investigate the global existence and boundedness of the unique positive classical solutions of the system in a bounded domain with smooth boundary and Neumann boundary conditions. Then, we analyze the local stability of the system and the existence of Hopf bifurcation. In addition, we prove the global asymptotic stability of steady states under some conditions by constructing a Lyapunov functional, and investigate convergence rates. Finally, we present several numerical simulations to illustrate the results.

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带有猎物-税收的比例依赖型食物链模型的动态分析

在本文中，我们考虑了一个食物链模型，该模型具有依赖比例的功能响应和猎物税。我们首先研究了该系统在具有光滑边界和诺伊曼边界条件的有界域中唯一正经典解的全局存在性和有界性。然后，我们分析了系统的局部稳定性和霍普夫分岔的存在性。此外，我们还通过构建 Lyapunov 函数证明了某些条件下稳态的全局渐近稳定性，并研究了收敛速率。最后，我们给出了几个数值模拟来说明结果。

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.