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Fixed-time synchronization of fractional-order Hopfield neural networks with proportional delays.

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Title: Fixed-time synchronization of fractional-order Hopfield neural networks with proportional delays.
Authors: Kumar, Pushpendra1,2 (AUTHOR) kumarsaraswatpk@gmail.com, Assali, El Abed1,3,4 (AUTHOR) elabed.assali@fsb.rnu.tn
Source: Mathematics & Computers in Simulation. Feb2026, Vol. 240, p367-380. 14p.
Subjects: Synchronization, Artificial neural networks, Lyapunov functions, Exponential functions, Feedback control systems, Numerical analysis
Abstract: This article explores the fixed-time synchronization of fractional-order Hopfield neural networks incorporating proportional delays. Unlike finite-time synchronization, where the convergence time varies based on the initial synchronization errors, fixed-time synchronization allows for a predetermined settling time that remains independent of initial conditions. To achieve fixed-time synchronization, two types of feedback control strategies incorporating fractional integrals are employed: one based on state feedback and another utilizing a controller designed with a Lyapunov function and an exponential function. By designing appropriate Lyapunov functions and employing inequality techniques, multiple sufficient conditions were established to guarantee the fixed-time synchronization of the considered systems under these control strategies. Finally, two numerical examples are presented to demonstrate the validity and practical relevance of the theoretical findings. [ABSTRACT FROM AUTHOR]
Copyright of Mathematics & Computers in Simulation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 188750610
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  Data: <searchLink fieldCode="DE" term="%22Synchronization%22">Synchronization</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+neural+networks%22">Artificial neural networks</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+functions%22">Lyapunov functions</searchLink><br /><searchLink fieldCode="DE" term="%22Exponential+functions%22">Exponential functions</searchLink><br /><searchLink fieldCode="DE" term="%22Feedback+control+systems%22">Feedback control systems</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink>
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  Data: This article explores the fixed-time synchronization of fractional-order Hopfield neural networks incorporating proportional delays. Unlike finite-time synchronization, where the convergence time varies based on the initial synchronization errors, fixed-time synchronization allows for a predetermined settling time that remains independent of initial conditions. To achieve fixed-time synchronization, two types of feedback control strategies incorporating fractional integrals are employed: one based on state feedback and another utilizing a controller designed with a Lyapunov function and an exponential function. By designing appropriate Lyapunov functions and employing inequality techniques, multiple sufficient conditions were established to guarantee the fixed-time synchronization of the considered systems under these control strategies. Finally, two numerical examples are presented to demonstrate the validity and practical relevance of the theoretical findings. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Mathematics & Computers in Simulation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.matcom.2025.07.035
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 14
        StartPage: 367
    Subjects:
      – SubjectFull: Synchronization
        Type: general
      – SubjectFull: Artificial neural networks
        Type: general
      – SubjectFull: Lyapunov functions
        Type: general
      – SubjectFull: Exponential functions
        Type: general
      – SubjectFull: Feedback control systems
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
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      – TitleFull: Fixed-time synchronization of fractional-order Hopfield neural networks with proportional delays.
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              Text: Feb2026
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              Y: 2026
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              Value: 240
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