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Compartmental Unpredictable Functions

Author

Listed:
  • Marat Akhmet

    (Department of Mathematics, Middle East Technical University, 06800 Ankara, Turkey)

  • Madina Tleubergenova

    (Department of Mathematics, Aktobe Regional University, Aktobe 030000, Kazakhstan
    Institute of Information and Computational Technologies, Almaty 050010, Kazakhstan)

  • Akylbek Zhamanshin

    (Department of Mathematics, Middle East Technical University, 06800 Ankara, Turkey)

Abstract

There is a huge family of recurrent functions, which starts with equilibria and ends with Poisson stable functions. They are fundamental in theoretical and application senses, and they admit a famous history. Recently, we have added the unpredictable functions to the family. The research has been performed in several papers and books. Obviously, theoretical and application merits of functions increase if one provides rigorously approved efficient methods of construction of concrete examples, as well as their numerical simulations. In the present study, we met the challenges for unpredictability by considering functions of two variables on diagonals. Algorithms have been created, and they are both deterministic and random. Characteristics are introduced to evaluate contributions of periodic and unpredictable components to the dynamics, and they are clearly illustrated in graphs of the functions. Definitions of non-periodic compartmental functions are provided as suggestions for the research in the future.

Suggested Citation

  • Marat Akhmet & Madina Tleubergenova & Akylbek Zhamanshin, 2023. "Compartmental Unpredictable Functions," Mathematics, MDPI, vol. 11(5), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1069-:d:1075164
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    References listed on IDEAS

    as
    1. Marat Akhmet & Duygu Aruğaslan Çinçin & Madina Tleubergenova & Zakhira Nugayeva, 2021. "Unpredictable Oscillations for Hopfield-Type Neural Networks with Delayed and Advanced Arguments," Mathematics, MDPI, vol. 9(5), pages 1-19, March.
    2. A. Kumar & R. P. Bhagat, 1987. "Poisson stability in product of dynamical systems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 10, pages 1-2, January.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Akhmet, Marat & Tleubergenova, Madina & Zhamanshin, Akylbek, 2024. "Cohen-Grossberg neural networks with unpredictable and Poisson stable dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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