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Adaptive Synchronization of a Category of Neural Networks with Proportional Delays

  • Qian Yan 1,   
  • Xiao Han 1,   
  • Liqun Zhou 1,2,*,   
  • Mengran Zheng 1,2

Received: 30 Sep 2025 | Revised: 08 Nov 2025 | Accepted: 17 Nov 2025 | Published: 24 Nov 2025

Abstract

This article delves into the adaptive synchronization of a category of proportional delay neural networks (PDNNs) in the drive-response framework, with a focus on exploring their global polynomial synchronization (GPS) and global asymptotic synchronization (GAS). By introducing polynomial functions, designing adaptive controllers, and constructing appropriate Lyapunov functional, the criteria for achieving adaptive synchronization in the studied system are obtained. Furthermore, the validity of the derived criteria is confirmed by means of a numerical example and simulations. Finally, the GPS control result of the numerical example is applied to the field of image encryption, and the effectiveness of adaptive control is verified through the application of image encryption.

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Yan, Q.; Han, X.; Zhou, L.; Zheng, M. Adaptive Synchronization of a Category of Neural Networks with Proportional Delays. Complex Systems Stability & Control 2025, 1 (1), 6.
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