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

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  • Chao Wang
  • Ravi P. Agarwal

Abstract

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.

Suggested Citation

  • Chao Wang & Ravi P. Agarwal, 2014. "A Further Study of Almost Periodic Time Scales with Some Notes and Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:267384
    DOI: 10.1155/2014/267384
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    References listed on IDEAS

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    1. Yongkun Li & Chao Wang, 2011. "Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-22, October.
    2. Yongkun Li & Chao Wang, 2011. "Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    3. Martin Bohner & Allan Peterson, 2001. "Dynamic Equations on Time Scales," Springer Books, Springer, number 978-1-4612-0201-1, October.
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    Cited by:

    1. Yongkun Li & Bing Li, 2015. "Almost Periodic Time Scales and Almost Periodic Functions on Time Scales," Journal of Applied Mathematics, John Wiley & Sons, vol. 2015(1).

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