Fixed/Predefined-time synchronization of memristor-based complex-valued BAM neural networks for image protection

Area of Science:

• Complex-valued neural networks
• Nonlinear dynamics
• Control theory

Background:

• Memristive complex-valued bidirectional associative memory neural networks (MCVBAMNNs) exhibit complex dynamics.
• Synchronization in such networks is crucial for applications but challenging due to time-varying delays.

Purpose of the Study:

• To investigate fixed-time and predefined-time synchronization for MCVBAMNNs with leakage time-varying delay.
• To develop a control strategy for achieving rapid and predictable synchronization.
• To explore the application of these synchronized networks in image encryption.

Main Methods:

• Transforming MCVBAMNNs into two real-valued systems.
• Designing a feedback controller utilizing Lyapunov stability theory and inequality techniques.
• Proposing a predefined-time stability theorem to directly link controller gain to synchronization time.

Main Results:

• An accurate upper bound for stability time estimation was derived.
• A novel predefined-time stability theorem was established, allowing arbitrary synchronization time setting.
• The developed chaotic MCVBAMNNs and synchronization technique were successfully applied to image encryption and decryption, demonstrating effectiveness.

Conclusions:

• The proposed control strategy effectively achieves fixed-time and predefined-time synchronization for MCVBAMNNs.
• The predefined-time synchronization theorem offers precise control over convergence time.
• The application in image encryption validates the theoretical findings and the security of the cryptographic system.