具有阶段结构和收获的单物种模型的分岔问题

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-06-24 DOI:10.1002/mma.11174

Honghua Bin, Yuying Liu, Junjie Wei

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引用次数: 0

摘要

本文研究了考虑阶段结构和收获的尼克尔森方程。利用Lambert W $$ W $$函数的性质，得到了正平衡点的存在性。利用特征方程中特征值的分布，得到了平衡点的局部稳定性和单种模型的Hopf分岔的存在性。进一步发现，当收获率足够小时，Hopf分岔在第一分岔值和最后分岔值处的方向分别为正向和反向，分岔周期解都是渐近稳定的。数值模拟验证了理论分析的正确性。

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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On Bifurcation of a Single-Species Model With Stage Structure and Harvest

In this paper, the Nicholson's blowflies equation with stage structure and harvest is investigated. By employing the property of Lambert $W$ function, the existence of positive equilibria is obtained. With aid of the distribution of the eigenvalues in the characteristic equation, the local stability of the equilibria and the existence of Hopf bifurcation of the single-species model are obtained. Furthermore, it is found that when the harvest rate is sufficiently small, the directions of the Hopf bifurcations at the first and last bifurcation values are forward and backward, respectively, and the bifurcating periodic solutions are all asymptotically stable. Numerical simulations are carried out to illustrate the theoretical analysis.

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.