Event-Based Synchronization Control for Memristive Neural Networks With Time-Varying Delay.

Area of Science:

• Control Theory
• Computational Neuroscience
• Nonlinear Dynamics

Background:

• Memristive neural networks (MNNs) are crucial for complex computations.
• Time-varying delays in MNNs pose significant challenges for synchronization.
• Existing control methods often incur high computational costs.

Purpose of the Study:

• To develop novel event-triggered control schemes for global synchronization of MNNs with time-varying delays.
• To reduce the computational burden of controllers through event-based strategies.
• To ensure the stability and synchronization of MNNs while avoiding Zeno behavior.

Main Methods:

• Introduction of a novel event-triggered controller with linear diffusive and discontinuous sign terms.
• Proposal of two event-based control schemes: static and dynamic event-triggering conditions.
• Derivation of sufficient conditions for ensuring synchronization between response and driving MNNs.
• Analysis to guarantee a positive lower bound for inter-execution time, preventing Zeno behavior.

Main Results:

• The proposed event-triggered controllers effectively achieve global synchronization for MNNs with time-varying delays.
• The static and dynamic event-triggering conditions significantly reduce controller computation costs.
• Sufficient conditions for synchronization are rigorously derived.
• A positive lower bound on inter-execution time is established, confirming the absence of Zeno behavior.

Conclusions:

• The developed event-triggered control strategies are effective for MNN synchronization.
• The proposed methods offer a computationally efficient approach to controlling MNNs with time-varying delays.
• Numerical simulations validate the theoretical findings and the practical applicability of the control schemes.