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Unpredictable Solutions of Linear Impulsive Systems

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 CS MES RK, Almaty 050000, Kazakhstan)

  • Mehmet Onur Fen

    (Department of Mathematics, TED University, 06420 Ankara, Turkey)

  • Zakhira Nugayeva

    (Department of Mathematics, Aktobe Regional University, Aktobe 030000, Kazakhstan
    Institute of Information and Computational Technologies CS MES RK, Almaty 050000, Kazakhstan)

Abstract

We consider a new type of oscillations of discontinuous unpredictable solutions for linear impulsive nonhomogeneous systems. The models under investigation are with unpredictable perturbations. The definition of a piecewise continuous unpredictable function is provided. The moments of impulses constitute a newly determined unpredictable discrete set. Theoretical results on the existence, uniqueness, and stability of discontinuous unpredictable solutions for linear impulsive differential equations are provided. We benefit from the B-topology in the space of discontinuous functions on the purpose of proving the presence of unpredictable solutions. For constructive definitions of unpredictable components in examples, randomly determined unpredictable sequences are newly utilized. Namely, the construction of a discontinuous unpredictable function is based on an unpredictable sequence determined by a discrete random process, and the set of discontinuity moments is realized by the logistic map. Examples with numerical simulations are presented to illustrate the theoretical results.

Suggested Citation

  • Marat Akhmet & Madina Tleubergenova & Mehmet Onur Fen & Zakhira Nugayeva, 2020. "Unpredictable Solutions of Linear Impulsive Systems," Mathematics, MDPI, vol. 8(10), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1798-:d:428939
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    References listed on IDEAS

    as
    1. 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.
    2. Zhao, Zhong & Li, Qiuying & Chen, Lansun, 2018. "Effect of rhizosphere dispersal and impulsive input on the growth of wetland plant," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 152(C), pages 69-80.
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    Cited by:

    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. António M. Lopes & J. A. Tenreiro Machado, 2022. "Nonlinear Dynamics," Mathematics, MDPI, vol. 10(15), pages 1-3, July.

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