Synchronization of the memristive recurrent neural networks via fuzzy adaptive strategy and its application

Lixia Ye; Qiling Zhao; Hang Zheng; Lixia Ye; Qiling Zhao; Hang Zheng

doi:10.3934/math.20261121

AIMS Mathematics

2026, Volume 11, Issue 9: 28097-28120. doi: 10.3934/math.20261121

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Research article

Synchronization of the memristive recurrent neural networks via fuzzy adaptive strategy and its application

1.
Department of Mathematics and Computer, Wuyi University, Wuyishan, 354300, China
2.
Fujian Key Laboratory of Big Data Application and Intellectualization for Tea Industry (Wuyi University), Digital Fujian Institute of Tourism Big Data (Wuyi University)

Received: 25 June 2026 Revised: 18 August 2026 Accepted: 21 August 2026 Published: 03 September 2026
MSC : 34E13, 34K35, 91B55

This study examines the synchronization issue for memristive recurrent neural networks (MRNNs) subject to random disturbances. Asymptotic synchronization and mean-square synchronization can be realized via the fuzzy adaptive strategy, whose adaptive rules are designed for the controller of the slave system, allowing iterative updates of its connection weights. The established synchronization criteria are applicable to various disturbance scenarios. Finally, the validity of the synchronization results are verified via multiple examples, further demonstrating that the proposed model with fuzzy adaptive strategy achieve higher SMD2 than 3-GMM and CNN in image enhancement. For the denoising of color images corrupted with noise intensities of $ 0.02 $ and $ 0.05 $, the proposed model yields higher EME and PSNR (over 30dB) values than BM3D, and its SMD2 values are closer to the original-image counterparts.
- synchronization,
- random disturbances,
- MRNNs,
- fuzzy adaptive strategy,
- image processing
Citation: Lixia Ye, Qiling Zhao, Hang Zheng. Synchronization of the memristive recurrent neural networks via fuzzy adaptive strategy and its application[J]. AIMS Mathematics, 2026, 11(9): 28097-28120. doi: 10.3934/math.20261121

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Abstract

This study examines the synchronization issue for memristive recurrent neural networks (MRNNs) subject to random disturbances. Asymptotic synchronization and mean-square synchronization can be realized via the fuzzy adaptive strategy, whose adaptive rules are designed for the controller of the slave system, allowing iterative updates of its connection weights. The established synchronization criteria are applicable to various disturbance scenarios. Finally, the validity of the synchronization results are verified via multiple examples, further demonstrating that the proposed model with fuzzy adaptive strategy achieve higher SMD2 than 3-GMM and CNN in image enhancement. For the denoising of color images corrupted with noise intensities of $ 0.02 $ and $ 0.05 $, the proposed model yields higher EME and PSNR (over 30dB) values than BM3D, and its SMD2 values are closer to the original-image counterparts.

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