A further study of almost periodic time scales with some notes and applications
type: Item
instance of: scholarly article
title: A further study of almost periodic time scales with some notes and applications
zbMATH Open document ID: 1470.34243
DOI: 10.1155/2014/267384
author: Chao Wang
author: Ravi P. Agarwal
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We introduce three equivalent concepts of almost periodic time scales as a further study of the corresponding concept proposed in [\textit{Y. Li} and the first author, Discrete Dyn. Nat. Soc. 2011, Article ID 727068, 20 p. (2011; Zbl 1232.26055)] and several examples of almost periodic time scales which are not periodic are provided. Furthermore, the concepts of almost periodic functions are redefined under the sense of this new timescale concept. Finally, almost periodicity of Cauchy matrix for dynamic equations is proved under these new definitions. Based on these results, the existence of almost periodic solutions to a class of nonlinear dynamic equations is investigated by the almost periodicity of Cauchy matrix on almost periodic time scales. Besides, as an application, we apply our results to a class of high-order Hopfield neural networks.
Mathematics Subject Classification ID: 34N05
Mathematics Subject Classification ID: 26E70
Mathematics Subject Classification ID: 34C27
zbMATH DE Number: 7022053
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/267384
OpenAlex ID: W2076754089
Wikidata QID: Q59037356
cites work: Uniformly almost periodic functions and almost periodic solutions to dynamic equations on time scales
cites work: Almost periodic functions on time scales and applications
cites work: Weighted pseudo almost automorphic functions with applications to abstract dynamic equations on time scales
cites work: Weighted piecewise pseudo almost automorphic functions with applications to abstract impulsive \(\nabla\)-dynamic equations on time scales
cites work: Almost periodic solutions of impulsive BAM neural networks with variable delays on time scales
cites work: Pseudo almost periodic functions and pseudo almost periodic solutions to dynamic equations on time scales
cites work: Almost automorphic solutions of dynamic equations on time scales
cites work: Almost periodic dynamics of a discrete Nicholson's blowflies model involving a linear harvesting term
cites work: Almost periodic solutions for second order dynamic equations on time scales
cites work: A connection between almost periodic functions defined on timescales and ℝ
cites work: Almost automorphic solutions of non-autonomous difference equations
cites work: Periodic solutions for a neutral nonlinear dynamical equation on a time scale
cites work: Partial dynamic equations on time scales
cites work: Q2723195
cites work: Dynamic equations on time scales: A survey
cites work: Almost periodic differential equations
description: scientific article; zbMATH DE number 7022053