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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

    as
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    2. 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.
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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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