Synchronization of fuzzy reaction–diffusion neural networks via semi-intermittent hybrid control

Kathiresan S. Kashkynbayev A. Mohanrasu S.S. Rajan R.
February 2025 Springer Nature

Journal of Applied Mathematics and Computing
2025 #71 Issue 1 1109 - 1139 pp.

This paper addresses the problem of synchronizing fuzzy reaction–diffusion neural networks (FRDNNs) with time-varying transmission delays using aperiodic semi-intermittent hybrid controls and explores its application within the realm of image encryption. The main challenge in analyzing the dynamics of FRDNNs included diffusion terms with uncertainty, and the inclusion of fuzzy logic operations further increases the system’s complexity. We propose a new concept called the average control width (ACW) for aperiodic semi-intermittent control (ASIC) systems; it is used in conjunction with the idea of average dwell time (ADT) for switched systems. A sufficient flexible condition for master–slave synchronization of neural networks using average-width semi-intermittent hybrid control assures ADT and ACW conditions. By utilizing these concepts, the proposed synchronization method can overcome the challenges posed by the diffusion terms and fuzzy logic operations in FRDNNs with time-varying transmission delays. Finally, the paper presents a theoretical framework for synchronizing FRDNNs with time-varying transmission delays using semi-intermittent hybrid control via LMI and suitable Lyapunov functional, validated through simulations. The proposed synchronization method is also applied to develop a novel chaos-based elliptic curve cryptography algorithm for medical image encryption.

Fuzzy reaction–diffusion neural networks , Image encryption , Linear matrix inequality , Semi-intermittent control , Synchronization

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Department of Mathematics, School of Sciences and Humanities, Nazarbayev University, Astana, 010000, Kazakhstan
Department of Mathematics, Bharathiar University, Tamil Nadu, Coimbatore, 641046, India

Department of Mathematics
Department of Mathematics

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