Higher order codimension bifurcations in a discrete-time toxic-phytoplankton–zooplankton model with Allee effect

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-10-06 DOI:10.1515/ijnsns-2021-0476

S. Salman, A. Elsadany

引用次数: 1

Abstract

Abstract In this paper, we use new methods to investigate different bifurcations of fixed points in a discrete-time toxic-phytoplankton–zooplankton model with Allee effect. The nonstandard discretization scheme produces a discrete analog of the continuous-time toxic-phytoplankton–zooplankton model with Allee effect. The local stability for proposed system around all of its fixed points is derived. We obtain the codimension-1 conditions of various bifurcations such as period doubling and Neimark–Sacker. Moreover, the system produces codimension-2 bifurcations such as resonance 1:1, 1:2, 1:3, and 1:4. Furthermore, the system can produce very rich dynamics, such as the existence of a semi-stable limit cycle, multiple coexisting periodic orbits, and chaotic behavior. Theoretical analysis is validated by numerical methods.

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具有Allee效应的离散时间有毒-浮游植物-浮游动物模型的高阶余维分岔

摘要在本文中，我们使用新的方法来研究具有Allee效应的离散时间有毒浮游植物-浮游动物模型中不动点的不同分叉。非标准离散化方案产生了具有Allee效应的连续时间有毒浮游植物-浮游动物模型的离散模拟。导出了系统在所有不动点附近的局部稳定性。我们得到了诸如倍周期和Neimark–Sacker等各种分叉的余维-1条件。此外，该系统产生余维2分叉，如共振1:1、1:2、1:3和1:4。此外，该系统可以产生非常丰富的动力学，如半稳定极限环的存在、多个共存的周期轨道和混沌行为。通过数值方法对理论分析进行了验证。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.