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Synchronisation analysis of fractional-order complex-valued BAM neural networks via machine learning-based largest Lyapunov exponent estimation
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DOI：10.1080/00207721.2026.2674843.png)
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Abstract
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This paper investigates the synchronisation problem of fractional-order complex-valued bidirectional associative memory neural networks (FCVBAMNNs) with time-varying delays. First, the drive response model is formulated using Caputo fractional derivatives, and the synchronisation error system is constructed under linear state-feedback control. By employing a fractional Lyapunov Krasovskii functional and the Lipschitz properties of complex activation functions, a sufficient condition ensuring global Mittag Leffler synchronisation is derived. The condition is expressed as a delay-dependent linear matrix inequality (LMI), and the corresponding static feedback controller is obtained through a matrix decomposition technique. To complement the analytical result, a machine learning (ML) framework is introduced to estimate the largest Lyapunov exponent (LLE) directly from simulated time-series data. Using a geometric mean absolute error (GMAE) based estimator, the ML model provides a data-driven approximation of the divergence rate of nearby trajectories, yielding a numerical indicator of synchronisation. Negative LLE values confirm the stability predicted by the LMI criterion. Numerical simulations of FCVBAMNNs demonstrate the effectiveness of the proposed controller and validate the agreement between theoretical Mittag-Leffler convergence and the ML-based LLE estimation. The combined analytical data-driven framework offers a reliable tool for understanding stability and synchronisation behaviours in fractional-order complex-valued neural networks.
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