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Strongly Unpredictable Oscillations of Hopfield-Type Neural Networks

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, Almaty 050000, Kazakhstan)

  • Zakhira Nugayeva

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

Abstract

In this paper, unpredictable oscillations in Hopfield-type neural networks is under investigation. The motion strongly relates to Poincaré chaos. Thus, the importance of the dynamics is indisputable for those problems of artificial intelligence, brain activity and robotics, which rely on chaos. Sufficient conditions for the existence and uniqueness of exponentially stable unpredictable solutions are determined. The oscillations continue the line of periodic and almost periodic motions, which already are verified as effective instruments of analysis and applications for image recognition, information processing and other areas of neuroscience. The concept of strongly unpredictable oscillations is a significant novelty of the present research, since the presence of chaos in each coordinate of the space state provides new opportunities in applications. Additionally to the theoretical analysis, we have provided strong simulation arguments, considering that all of the assumed conditions are fulfilled.

Suggested Citation

  • Marat Akhmet & Madina Tleubergenova & Zakhira Nugayeva, 2020. "Strongly Unpredictable Oscillations of Hopfield-Type Neural Networks," Mathematics, MDPI, vol. 8(10), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1791-:d:428483
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    References listed on IDEAS

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    1. Yuan, Quan & Li, Qingdu & Yang, Xiao-Song, 2009. "Horseshoe chaos in a class of simple Hopfield neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1522-1529.
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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. 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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