Finite-Time and Fixed-Time Synchronization of Delayed Memristive Neural Networks via Adaptive Aperiodically...

Area of Science:

• Control Theory
• Computational Neuroscience
• Nonlinear Dynamics

Background:

• Memristive neural networks (MNNs) exhibit complex dynamics crucial for advanced computing.
• Achieving synchronization in MNNs with time-varying delays is challenging.
• Existing synchronization methods often lack guaranteed finite-time or fixed-time convergence.

Purpose of the Study:

• To investigate finite-time and fixed-time synchronization for MNNs with mixed time-varying delays.
• To develop an adaptive aperiodically intermittent adjustment strategy for MNN synchronization.
• To establish sufficient conditions for guaranteed synchronization and estimate settling times.

Main Methods:

• Utilizing theories of set-valued mappings and differential inclusions to derive error MNNs.
• Applying Lyapunov function method and Linear Matrix Inequality (LMI) techniques for stability analysis.
• Designing an adaptive updating law for the aperiodically intermittent control strategy.

Main Results:

• Derived sufficient conditions for achieving both finite-time and fixed-time synchronization in MNNs.
• Explicitly estimated the settling time for the synchronization process.
• Demonstrated the effectiveness of the proposed control strategy through three numerical examples.

Conclusions:

• The proposed adaptive aperiodically intermittent control strategy effectively guarantees finite-time and fixed-time synchronization for MNNs with mixed delays.
• The theoretical results provide a robust framework for controlling complex memristive systems.
• The explicit settling time estimation offers practical insights for real-world applications.