有理图的动力学:无界循环、无界混沌间隔和组织中心

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-09-13 DOI:10.1080/10236198.2023.2253329

Laura Gardini, Iryna Sushko, Wirot Tikjha

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引用次数: 0

摘要

考虑了依赖于两个参数A和b的一维有理映射f(x)=(x2−A)/(x2−b)。由于超稳定的无界循环(即在无穷远处有一个点的周期轨道，与垂直渐近线相关)以及无界混沌区间所发生的无界循环，证明了有理图特有的分支序列。此外，研究了在(a,b)参数平面上具有组织中心作用的两个特殊分岔点。每个点都与一对条件有关，这使我们能够将它们视为共维-2的分岔点，因为这类组织中心通常是这样的。然而，这两个条件不是与分岔有关，而是与函数图中的退化有关。利用有理映射的特殊性质，用解析和数值方法研究了与这些特殊点相关的引起吸引环的分岔序列。

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Dynamics of a rational map: unbounded cycles, unbounded chaotic intervals and organizing centres

A one-dimensional rational map f(x)=(x2−a)/(x2−b) depending on the two parameters a and b is considered. Sequences of bifurcations peculiar of rational maps are evidenced, as those occurring due to unbounded cycles (that is, periodic orbits having one point at infinity, related to the vertical asymptotes) that are superstable, as well as to unbounded chaotic intervals. Moreover, two particular bifurcation points, having the role of organizing centres in the (a,b)-parameter plane, are studied. Each point is related to a pair of conditions, which allow us to consider them as the bifurcation points of codimension-2, as it is usual for this kind of organizing centres. However, the two conditions are related not to bifurcations but to degeneracies in the graph of the function. The sequences of bifurcations leading to attracting cycles associated with these particular points are investigated, analytically and numerically, making use of particular properties of the rational map.

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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.