Adaptive Synchronization of Reaction-Diffusion Neural Networks and Its Application to Secure Communication.

Area of Science:

• Control Systems Engineering
• Applied Mathematics
• Information Security

Background:

• Reaction-diffusion neural networks (RDNNs) with delays present complex dynamics.
• Synchronization of these networks is crucial for secure communication applications.
• Existing methods for synchronization may have limitations in practical implementation.

Purpose of the Study:

• To design an adaptive control strategy for synchronizing RDNNs with delays.
• To develop robust synchronization criteria applicable to image secure communications.
• To enhance image encryption algorithms using the synchronization properties of RDNNs.

Main Methods:

• Design of an adaptive controller without a sign function, featuring a time-varying gain matrix.
• Establishment of synchronization criteria using linear matrix inequalities (LMIs).
• Construction of a novel Lyapunov-Krasovskii functional, Green's formula, and Wirtinger's inequality.

Main Results:

• Guaranteed global asymptotic synchronization of the error model under proposed sufficient conditions.
• Numerical illustrations validating the effectiveness of the derived synchronization criteria.
• Demonstration of improved image transaction security via chaotic RDNN dynamics and a two-level encryption (watermarking and diffusion).

Conclusions:

• The proposed adaptive control and synchronization criteria are effective for RDNNs with delays.
• The method offers enhanced security for image communication.
• The study contributes novel techniques to both neural network synchronization and image encryption.