Global Attractors for a Class of Discrete Dynamical Systems

IF 1.4 4区数学 Q1 MATHEMATICS

Journal of Dynamics and Differential Equations 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

Journal of Dynamics and Differential Equations 数学-数学

CiteScore

3.30

自引率

7.70%

发文量

116

审稿时长

>12 weeks

期刊介绍： Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.