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Almost Periodic Solutions to Dynamic Equations on Time Scales and Applications

Author

Listed:
  • Yongkun Li
  • Chao Wang

Abstract

We first introduce the concept of admitting an exponential dichotomy to a class of linear dynamic equations on time scales and study the existence and uniqueness of almost periodic solution and its expression form to this class of linear dynamic equations on time scales. Then, as an application, using these concepts and results, we establish sufficient conditions for the existence and exponential stability of almost periodic solution to a class of Hopfield neural networks with delays. Finally, two examples and numerical simulations given to illustrate our results are plausible and meaningful.

Suggested Citation

  • Yongkun Li & Chao Wang, 2012. "Almost Periodic Solutions to Dynamic Equations on Time Scales and Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:463913
    DOI: 10.1155/2012/463913
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    References listed on IDEAS

    as
    1. 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).
    2. 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.
    3. Martin Bohner & Allan Peterson, 2001. "Dynamic Equations on Time Scales," Springer Books, Springer, number 978-1-4612-0201-1, March.
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    Cited by:

    1. Zhinan Xia, 2014. "Discrete Weighted Pseudo‐Almost Automorphy and Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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