Strange attractors in a predator–prey system with non-monotonic response function and periodic perturbation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2019-01-01 DOI:10.3934/jcd.2019024

J. M. Tuwankotta, Eric Harjanto

引用次数: 2

Abstract

A system of ordinary differential equations of a predator–prey type, depending on nine parameters, is studied. We have included in this model a nonmonotonic response function and time periodic perturbation. Using numerical continuation software, we have detected three codimension two bifurcations for the unperturbed system, namely cusp, Bogdanov-Takens and Bautin bifurcations. Furthermore, we concentrate on two regions in the parameter space, the region where the Bogdanov-Takens and the region where Bautin bifurcations occur. As we turn on the time perturbation, we find strange attractors in the neighborhood of invariant tori of the unperturbed system.

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具有非单调响应函数和周期扰动的捕食-食饵系统中的奇异吸引子

研究了一类具有9个参数的捕食者-猎物型常微分方程组。在该模型中加入了非单调响应函数和时间周期扰动。利用数值延拓软件，我们检测了非摄动系统的三个余维二分岔，即cusp分岔、Bogdanov-Takens分岔和Bautin分岔。此外，我们集中在参数空间中的两个区域，即Bogdanov-Takens区域和Bautin分岔发生的区域。当我们打开时间摄动时，我们在无摄动系统的不变环面邻域中发现了奇异吸引子。

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.