Global stability in the Ricker model with delay and stocking

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-03 DOI:10.1002/mma.10440

Ziyad AlSharawi, Sadok Kallel

引用次数: 0

Abstract

We consider the Ricker model with delay and constant or periodic stocking. We found that the high stocking density tends to neutralize the delay effect on stability. Conditions are established on the parameters to ensure the global stability of the equilibrium solution in the case of constant stocking, as well as the global stability of the 2-periodic solution in the case of 2-periodic stocking. Our approach extensively relies on the utilization of the embedding technique. Whether constant stocking or periodic stocking, the model has the potential to undergo a Neimark–Sacker bifurcation in both cases. However, the Neimark–Sacker bifurcation in the 2-periodic case results in the emergence of two invariant curves that collectively function as a single attractor. Finally, we pose open questions in the form of conjectures about global stability for certain choices of the parameters.

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有延迟和存量的里克尔模型的总体稳定性

我们考虑了具有延迟和恒定或周期放养的 Ricker 模型。我们发现，高密度放养往往会中和延迟对稳定性的影响。我们建立了参数条件，以确保恒定放养情况下平衡解的全局稳定性，以及双周期放养情况下双周期解的全局稳定性。我们的方法广泛依赖于嵌入技术的使用。无论是恒定放养还是周期放养，模型在两种情况下都有可能出现 Neimark-Sacker 分岔。然而，在双周期情况下，Neimark-Sacker 分岔会导致出现两条不变曲线，它们共同作为一个吸引子。最后，我们以猜想的形式提出了关于某些参数选择下全局稳定性的开放性问题。

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

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.