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Dynamics of the Almost Periodic Discrete Mackey–Glass Model

Author

Listed:
  • Zhijian Yao

    (Department of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China)

  • Jehad Alzabut

    (Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia)

  • Debaldev Jana

    (Department of Mathematics & SRM Research Institute, SRM Institute of Science and Technology, Kattankulathur, 603 203 TamilNadu, India)

Abstract

This paper is concerned with a class of the discrete Mackey–Glass model that describes the process of the production of blood cells. Prior to proceeding to the main results, we prove the boundedness and extinction of its solutions. By means of the contraction mapping principle and under appropriate assumptions, we prove the existence of almost periodic positive solutions. Furthermore and by the implementation of the discrete Lyapunov functional, sufficient conditions are established for the exponential convergence of the almost periodic positive solution. Examples, as well as numerical simulations are illustrated to demonstrate the effectiveness of the theoretical findings of the paper. Our results are new and generalize some previously-reported results in the literature.

Suggested Citation

  • Zhijian Yao & Jehad Alzabut & Debaldev Jana, 2018. "Dynamics of the Almost Periodic Discrete Mackey–Glass Model," Mathematics, MDPI, vol. 6(12), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:12:p:333-:d:191217
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    References listed on IDEAS

    as
    1. McCrorie, J. Roderick, 2000. "Deriving The Exact Discrete Analog Of A Continuous Time System," Econometric Theory, Cambridge University Press, vol. 16(6), pages 998-1015, December.
    2. Yongkun Li & Chao Wang, 2011. "Almost Periodic Functions on Time Scales and Applications," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-20, July.
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