具有两个延迟和 Michaelis-Menten 型捕食者收获的野内猎物-捕食者渔业模型的稳定性和霍普夫分岔。

IF 2.6 4区 工程技术 Q1 Mathematics
Min Hou, Tonghua Zhang, Sanling Yuan
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引用次数: 0

摘要

在本文中,我们提出并研究了一个包含两个延迟和基于迈克尔-门顿原理的收获机制的野内捕食者-猎物系统,并假设两个物种竞争一个共享资源。首先,我们研究了相关特征方程的性质,推导出延迟模型中均衡渐近稳定性和霍普夫分岔存在的充分条件。利用正态形式方法和中心流形定理,我们分析了霍普夫分岔产生的周期解的稳定性和方向。随后,我们通过数值模拟验证了我们的理论发现。此外,我们还探讨了收割对生物资源数量的影响,并研究了与两个延迟相关的临界值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Stability and Hopf bifurcation of an intraguild prey-predator fishery model with two delays and Michaelis-Menten type predator harvest.

In this paper, we have proposed and investigated an intraguild predator-prey system incorporating two delays and a harvesting mechanism based on the Michaelis-Menten principle, and it was assumed that the two species compete for a shared resource. Firstly, we examined the properties of the relevant characteristic equations to derive sufficient conditions for the asymptotical stability of equilibria in the delayed model and the existence of Hopf bifurcation. Using the normal form method and the central manifold theorem, we analyzed the stability and direction of periodic solutions arising from Hopf bifurcations. Our theoretical findings were subsequently validated through numerical simulations. Furthermore, we explored the impact of harvesting on the quantity of biological resources and examined the critical values associated with the two delays.

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来源期刊
Mathematical Biosciences and Engineering
Mathematical Biosciences and Engineering 工程技术-数学跨学科应用
CiteScore
3.90
自引率
7.70%
发文量
586
审稿时长
>12 weeks
期刊介绍: Mathematical Biosciences and Engineering (MBE) is an interdisciplinary Open Access journal promoting cutting-edge research, technology transfer and knowledge translation about complex data and information processing. MBE publishes Research articles (long and original research); Communications (short and novel research); Expository papers; Technology Transfer and Knowledge Translation reports (description of new technologies and products); Announcements and Industrial Progress and News (announcements and even advertisement, including major conferences).
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