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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]
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Database: Engineering Source
Description
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]
ISSN:03784754
DOI:10.1016/j.matcom.2025.07.035