具有通性捕食者和恒产收获的霍林-坦纳模型的分岔分析

IF 1.9 4区 数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Hongqiuxue Wu, Zhong Li, Mengxin He
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引用次数: 0

摘要

在本文中,我们将恒定产量的猎物捕获引入到具有通才捕食者的霍林-坦纳模型中。我们证明了唯一的正平衡是一个标度为 4 的尖顶。随着参数值的变化,该系统会出现标度为 4 的退化 Bogdanov-Takens 分岔。利用结果消元法,我们证明正平衡是一个阶数为 2 的弱焦点,系统经历了标度为 2 的退化霍普夫分岔,并有两个极限循环。通过数值模拟,我们证明了随着参数的变化,系统会出现同室分岔和极限循环的鞍节点分岔。主要结果表明,恒定产量的猎物捕获和通性捕食者会导致模型的复杂动态行为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Bifurcation Analysis of a Holling–Tanner Model with Generalist Predator and Constant-Yield Harvesting

In this paper, we introduce constant-yield prey harvesting into the Holling–Tanner model with generalist predator. We prove that the unique positive equilibrium is a cusp of codimension 4. As the parameter values change, the system exhibits degenerate Bogdanov–Takens bifurcation of codimension 4. Using the resultant elimination method, we show that the positive equilibrium is a weak focus of order 2, and the system undergoes degenerate Hopf bifurcation of codimension 2 and has two limit cycles. By numerical simulations, we demonstrate that the system exhibits homoclinic bifurcation and saddle–node bifurcation of limit cycles as the parameters are varied. The main results show that constant-yield prey harvesting and generalist predator can lead to complex dynamic behavior of the model.

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来源期刊
International Journal of Bifurcation and Chaos
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.
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