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Stability and Synchronization of Fractional-Order Complex-Valued Inertial Neural Networks: A Direct Approach

Author

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  • Hualin Song

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China)

  • Cheng Hu

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China)

  • Juan Yu

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China)

Abstract

This paper is dedicated to the asymptotic stability and synchronization for a type of fractional complex-valued inertial neural network by developing a direct analysis method. First, a new fractional differential inequality is presented for nonnegative functions, which provides an effective tool for the convergence analysis of fractional-order systems. Moreover, instead of the previous separation analysis for complex-valued neural networks, a class of Lyapunov functions composed of the complex-valued states and their fractional derivatives is constructed, and some compact stability criteria are derived. In synchronization analysis, unlike the existing control schemes for reduced-order subsystems, some feedback and adaptive control schemes, formed by the linear part and the fractional derivative part, are directly designed for the response fractional inertial neural networks, and some synchronization conditions are derived using the established fractional inequality. Finally, the theoretical analysis is supported via two numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4823-:d:1007796
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    References listed on IDEAS

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    1. Ravi Agarwal & Snezhana Hristova, 2022. "Impulsive Memristive Cohen–Grossberg Neural Networks Modeled by Short Term Generalized Proportional Caputo Fractional Derivative and Synchronization Analysis," Mathematics, MDPI, vol. 10(13), pages 1-12, July.
    2. Chen, Dazhao & Zhang, Zhengqiu, 2022. "Globally asymptotic synchronization for complex-valued BAM neural networks by the differential inequality way," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Marat Akhmet & Madina Tleubergenova & Akylbek Zhamanshin, 2020. "Inertial Neural Networks with Unpredictable Oscillations," Mathematics, MDPI, vol. 8(10), pages 1-11, October.
    4. Yaning Yu & Ziye Zhang, 2022. "State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays," Mathematics, MDPI, vol. 10(10), pages 1-14, May.
    5. Wei, Xiaofeng & Zhang, Ziye & Lin, Chong & Chen, Jian, 2021. "Synchronization and anti-synchronization for complex-valued inertial neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    6. Rathinasamy, Anandaraman & Mayavel, Pichamuthu, 2023. "Strong convergence and almost sure exponential stability of balanced numerical approximations to stochastic delay Hopfield neural networks," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    7. Bai, Zhenguo & Yang, Tianhui, 2022. "Spreading speeds of cellular neural networks model with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    8. Mohammad Hosein Sabzalian & Khalid A. Alattas & Fayez F. M. El-Sousy & Ardashir Mohammadzadeh & Saleh Mobayen & Mai The Vu & Mauricio Aredes, 2022. "A Neural Controller for Induction Motors: Fractional-Order Stability Analysis and Online Learning Algorithm," Mathematics, MDPI, vol. 10(6), pages 1-17, March.
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    Cited by:

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    2. Xinsong Yang & Ruofeng Rao, 2023. "Well-Posedness, Dynamics, and Control of Nonlinear Differential System with Initial-Boundary Value," Mathematics, MDPI, vol. 11(10), pages 1-4, May.

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