A Further Study of Almost Periodic Time Scales with Some Notes and Applications

We introduce three equivalent concepts of almost periodic time scales as a further study of the corresponding concept proposed in Li and Wang (2011) and several examples of almost periodic time scales which are not periodic are provided. Furthermore, the concepts of almost periodic functions are red...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2014-01, Vol.2014 (2014), p.192-202-319
Main Authors: Wang, Chao, Agarwal, Ravi P.
Format: Article
Language:English
Subjects:
Banach spaces
Differential equations
Hypotheses
Mathematical research
Mathematics
Matrices
Meteorology
Neural networks
Periodic functions
Studies
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Summary:We introduce three equivalent concepts of almost periodic time scales as a further study of the corresponding concept proposed in Li and Wang (2011) 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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/267384