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Inertial Neural Networks with Unpredictable Oscillations

Author

Listed:
  • Marat Akhmet

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

  • Madina Tleubergenova

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

  • Akylbek Zhamanshin

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

Abstract

In this paper, inertial neural networks are under investigation, that is, the second order differential equations. The recently introduced new type of motions, unpredictable oscillations, are considered for the models. The motions continue a line of periodic and almost periodic oscillations. The research is of very strong importance for neuroscience, since the existence of unpredictable solutions proves Poincaré chaos. Sufficient conditions have been determined for the existence, uniqueness, and exponential stability of unpredictable solutions. The results can significantly extend the role of oscillations for artificial neural networks exploitation, since they provide strong new theoretical and practical opportunities for implementation of methods of chaos extension, synchronization, stabilization, and control of periodic motions in various types of neural networks. Numerical simulations are presented to demonstrate the validity of the theoretical results.

Suggested Citation

  • Marat Akhmet & Madina Tleubergenova & Akylbek Zhamanshin, 2020. "Inertial Neural Networks with Unpredictable Oscillations," Mathematics, MDPI, vol. 8(10), pages 1-11, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1797-:d:428925
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    Citations

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    Cited by:

    1. Hualin Song & Cheng Hu & Juan Yu, 2022. "Stability and Synchronization of Fractional-Order Complex-Valued Inertial Neural Networks: A Direct Approach," Mathematics, MDPI, vol. 10(24), pages 1-23, December.

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