Global Attractors for a Class of Discrete Dynamical Systems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-25 DOI:10.1007/s10884-024-10356-9

引用次数: 0

Abstract

In this paper, we study the existence of global attractors for a class of discrete dynamical systems naturally originated from impulsive dynamical systems. We establish sufficient conditions for the existence of a discrete global attractor. Moreover, we investigate the relationship among different types of global attractors, i.e., the attractor \({\mathcal {A}}\) of a continuous dynamical system, the attractor \(\tilde{{\mathcal {A}}}\) of an impulsive dynamical system and the attractor \(\hat{{\mathcal {A}}}\) of a discrete dynamical system. Two applications are presented, one involving an integrate-and-fire neuron model, and the other involving a nonlinear reaction-diffusion initial boundary value problem.

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一类离散动力系统的全局吸引子

摘要本文研究了一类离散动力系统的全局吸引子的存在问题，该系统自然来源于脉冲动力系统。我们建立了离散全局吸引子存在的充分条件。此外，我们还研究了不同类型的全局吸引子之间的关系，即连续动力系统的吸引子（\({\mathcal {A}}\) ）、冲动动力系统的吸引子（\(\tilde{\mathcal {A}}\) ）和离散动力系统的吸引子（\(\hat{\mathcal {A}}\) ）。本文介绍了两个应用，一个涉及集成-发射神经元模型，另一个涉及非线性反应-扩散初始边界值问题。

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

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.