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Uniformly rd-piecewise almost periodic functions with applications to the analysis of impulsive Δ-dynamic system on time scales

Author

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  • Wang, Chao
  • Agarwal, Ravi P.

Abstract

In the present work, we introduce two equivalent concepts of uniformly rd-piecewise almost periodic functions on time scales and their equivalence is proved, based on this, some basic properties of them are obtained. Then, some new criteria of exponential dichotomy are established for homogeneous Δ-dynamic system on time scales. Also, some completely new theorems are established on time scales for impulsive almost periodic dynamic systems such as Favard’s theorem and exponential dichotomy theorem. As applications, we provide a method to obtain an almost periodic solution for a given nonhomogeneous impulsive dynamic system. Furthermore, we introduce an impulsive non-autonomous Nicholson’s blowflies system model with patch structure and multiple nonlinear harvesting terms for which the existence and exponential stability of almost periodic solutions are studied, which shows that our results can be applied feasibly and effectively.

Suggested Citation

  • Wang, Chao & Agarwal, Ravi P., 2015. "Uniformly rd-piecewise almost periodic functions with applications to the analysis of impulsive Δ-dynamic system on time scales," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 271-292.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:271-292
    DOI: 10.1016/j.amc.2015.02.054
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    Cited by:

    1. Wang, Chao & Agarwal, Ravi P. & O’Regan, Donal, 2022. "Almost periodic fuzzy multidimensional dynamic systems and applications on time scales," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Chao Wang & Rathinasamy Sakthivel & Gaston M. N’Guérékata, 2020. "S -Almost Automorphic Solutions for Impulsive Evolution Equations on Time Scales in Shift Operators," Mathematics, MDPI, vol. 8(6), pages 1-28, June.
    3. Chao Wang & Ravi P. Agarwal & Donal O’Regan & Gaston M. N’Guérékata, 2019. "n 0 -Order Weighted Pseudo Δ-Almost Automorphic Functions and Abstract Dynamic Equations," Mathematics, MDPI, vol. 7(9), pages 1-25, August.
    4. Chao Wang & Ravi P. Agarwal & Donal O’Regan, 2019. "δ -Almost Periodic Functions and Applications to Dynamic Equations," Mathematics, MDPI, vol. 7(6), pages 1-27, June.

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