Fixed-Time Pinning Common Synchronization and Adaptive Synchronization for Delayed Quaternion-Valued Neural Networks

Area of Science:

• * Control Theory
• * Computational Neuroscience
• * Artificial Intelligence

Background:

• * Synchronization is crucial for complex systems like neural networks.
• * Time-varying delays and quaternion-valued dynamics present significant control challenges.
• * Existing methods may lack efficiency in convergence time and adaptability.

Purpose of the Study:

• * To develop fixed-time pinning control for quaternion-valued neural networks (QVNNs).
• * To achieve adaptive synchronization with self-regulating controllers.
• * To establish criteria for fixed-time common and adaptive synchronization.

Main Methods:

• * Application of fixed-time control theory to design pinning controllers.
• * Utilization of Lyapunov function approach and inequality techniques.
• * Development of adaptive controllers with automatic gain adjustment.

Main Results:

• * Established fixed-time common synchronization criteria for QVNNs with time-varying delays.
• * Achieved fixed-time adaptive synchronization using self-regulating controllers.
• * Demonstrated the effectiveness of the proposed methods through simulation examples.

Conclusions:

• * The proposed fixed-time pinning control strategies ensure rapid and efficient synchronization in QVNNs.
• * Adaptive controllers offer enhanced self-regulation capabilities for improved performance.
• * The findings provide valuable theoretical and practical insights for synchronizing complex neural network systems.