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Almost periodic solutions for quaternion-valued shunting inhibitory cellular neural networks of neutral type with time delays in the leakage term

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  • Yongkun Li
  • Xiaofang Meng

Abstract

In this paper, we propose a class of quaternion-valued shunting inhibitory cellular neural networks of neutral type with time delays in the leakage term. In order to overcome the difficulty of the non-commutativity of quaternion multiplication, we first decompose the system under consideration into four real-valued systems. Then by using the exponential dichotomy theory of linear differential equations and Banach's fixed point theorem, we establish sufficient conditions to ensure the existence and global exponential stability of almost periodic solutions for this class of neural networks. Finally, a numerical example is given to demonstrate the effectiveness of the obtained result.

Suggested Citation

  • Yongkun Li & Xiaofang Meng, 2018. "Almost periodic solutions for quaternion-valued shunting inhibitory cellular neural networks of neutral type with time delays in the leakage term," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(11), pages 2490-2505, August.
    • Handle: RePEc:taf:tsysxx:v:49:y:2018:i:11:p:2490-2505
    DOI: 10.1080/00207721.2018.1505006
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    Cited by:

    1. Rajchakit, G. & Sriraman, R. & Lim, C.P. & Unyong, B., 2022. "Existence, uniqueness and global stability of Clifford-valued neutral-type neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 508-527.
    2. Marat Akhmet & Madina Tleubergenova & Akylbek Zhamanshin, 2023. "Shunting Inhibitory Cellular Neural Networks with Compartmental Unpredictable Coefficients and Inputs," Mathematics, MDPI, vol. 11(6), pages 1-18, March.
    3. Stamov, Gani & Stamova, Ivanka & Martynyuk, Anatoliy & Stamov, Trayan, 2021. "Almost periodic dynamics in a new class of impulsive reaction–diffusion neural networks with fractional-like derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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