A further study of almost periodic time scales with some notes and applications. (English) Zbl 1470.34243

Wang, Chao; Agarwal, Ravi P.

Abstr. Appl. Anal. 2014, Article ID 267384, 11 p. (2014).

Summary: We introduce three equivalent concepts of almost periodic time scales as a further study of the corresponding concept proposed in [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.

MSC:

34N05	Dynamic equations on time scales or measure chains
26E70	Real analysis on time scales or measure chains
34C27	Almost and pseudo-almost periodic solutions to ordinary differential equations

Citations:

Zbl 1232.26055

References:

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