探索迭代隐函数系统：吸引力的存在与特性

IF 1.9 4区数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

International Journal of Bifurcation and Chaos Pub Date : 2024-04-09 DOI:10.1142/s0218127424500597

Zhong Dai, Shutang Liu

引用次数: 0

摘要

本文研究了一种由方程 Fn(x,y)=c 组成的迭代隐函数系统，其中 Fn(x,y) 是连续函数，c 是常数。根据不同的方程条件，包括方程 Fn(x,y)=c 包含隐函数或对 y 具有 αn 契约性，证明了迭代隐函数系统吸引子的存在性。同时，我们给出了隐函数收敛和迭代隐函数系统单调序列的定义。最后，阐明了迭代隐函数系统吸引子的一些性质。

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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Exploring Iterated Implicit Function Systems: Existence and Properties of Attractors

This paper investigates a type of iterated implicit function systems composed of equations $F_{n} (x, y) = c$ , where $F_{n} (x, y)$ is a continuous function, and $c$ is a constant. The existence of attractors of iterated implicit function systems is proved based on different equation conditions, including the equation $F_{n} (x, y) = c$ containing the implicit function or being $α_{n}$ -contractive about $y$ . Meanwhile, we give definitions of implicit convergence of functions and monotone sequence of iterated implicit function systems. Finally, some properties of attractors of iterated implicit function systems are elucidated.

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来源期刊

International Journal of Bifurcation and Chaos 数学-数学跨学科应用

CiteScore

4.10

自引率

13.60%

发文量

237

审稿时长

2-4 weeks

期刊介绍： The International Journal of Bifurcation and Chaos is widely regarded as a leading journal in the exciting fields of chaos theory and nonlinear science. Represented by an international editorial board comprising top researchers from a wide variety of disciplines, it is setting high standards in scientific and production quality. The journal has been reputedly acclaimed by the scientific community around the world, and has featured many important papers by leading researchers from various areas of applied sciences and engineering. The discipline of chaos theory has created a universal paradigm, a scientific parlance, and a mathematical tool for grappling with complex dynamical phenomena. In every field of applied sciences (astronomy, atmospheric sciences, biology, chemistry, economics, geophysics, life and medical sciences, physics, social sciences, ecology, etc.) and engineering (aerospace, chemical, electronic, civil, computer, information, mechanical, software, telecommunication, etc.), the local and global manifestations of chaos and bifurcation have burst forth in an unprecedented universality, linking scientists heretofore unfamiliar with one another''s fields, and offering an opportunity to reshape our grasp of reality.