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Cohen-Grossberg neural networks with unpredictable and Poisson stable dynamics

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  • Akhmet, Marat
  • Tleubergenova, Madina
  • Zhamanshin, Akylbek

Abstract

In this paper, we provide theoretical as well as numerical results concerning recurrent oscillations in Cohen-Grossberg neural networks with variable inputs and strengths of connectivity for cells, which are unpredictable or Poisson stable functions. A special case of the compartmental coefficients with periodic and unpredictable ingredients is also carefully researched. By numerical and graphical analysis, it is shown how a constructive technical characteristic, the degree of periodicity, reflects contributions of the ingredients to final outputs of the neural networks. Sufficient conditions are obtained to guarantee the existence of exponentially stable unpredictable outputs of the models. They are specified for Poisson stability by utilizing the original method of included intervals. Examples with numerical simulations that support the theoretical results are provided.

Suggested Citation

  • Akhmet, Marat & Tleubergenova, Madina & Zhamanshin, Akylbek, 2024. "Cohen-Grossberg neural networks with unpredictable and Poisson stable dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:chsofr:v:178:y:2024:i:c:s0960077923012092
    DOI: 10.1016/j.chaos.2023.114307
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    References listed on IDEAS

    as
    1. Marat Akhmet & Kağan Başkan & Cihan Yeşil, 2023. "Revealing Chaos Synchronization Below the Threshold in Coupled Mackey–Glass Systems," Mathematics, MDPI, vol. 11(14), pages 1-15, July.
    2. Kong, Fanchao & Ren, Yong & Sakthivel, Rathinasamy, 2021. "New criteria on periodicity and stabilization of discontinuous uncertain inertial Cohen-Grossberg neural networks with proportional delays," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Akhmet, Marat & Yeşil, Cihan & Başkan, Kağan, 2023. "Synchronization of chaos in semiconductor gas discharge model with local mean energy approximation," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    4. Chen, Qun & Li, Bo & Yin, Wei & Jiang, Xiaowei & Chen, Xiangyong, 2023. "Bifurcation, chaos and fixed-time synchronization of memristor cellular neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    5. Marat Akhmet & Madina Tleubergenova & Akylbek Zhamanshin, 2023. "Compartmental Unpredictable Functions," Mathematics, MDPI, vol. 11(5), pages 1-17, February.
    6. Sun, Ying & Zhang, Luying & Yao, Minghui, 2023. "Chaotic time series prediction of nonlinear systems based on various neural network models," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    7. Marat Akhmet & Madina Tleubergenova & Zakhira Nugayeva, 2020. "Strongly Unpredictable Oscillations of Hopfield-Type Neural Networks," Mathematics, MDPI, vol. 8(10), pages 1-14, October.
    8. Xiaohu Li & Feng Xu & Jinhua Zhang & Sunan Wang, 2013. "A Multilayer Feed Forward Small-World Neural Network Controller and Its Application on Electrohydraulic Actuation System," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, June.
    9. Chen, Ling & Zhao, Hongyong, 2008. "Global stability of almost periodic solution of shunting inhibitory cellular neural networks with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 351-357.
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