Matrix Measure-Based Event-Triggered Impulsive Quasi-Synchronization on Coupled Neural Networks

Area of Science:

• Control Theory
• Computational Neuroscience
• Systems Engineering

Background:

• Coupled neural networks are crucial in modeling complex systems.
• Time-varying delays and random uncertainties pose significant challenges to network synchronization.
• Existing control methods often struggle with these complex network dynamics.

Purpose of the Study:

• To investigate quasi-synchronization in coupled neural networks with time-varying delays and random uncertainties.
• To develop a novel event-triggered impulsive control approach for enhanced network stability.
• To ensure synchronization within a defined error bound, addressing practical limitations.

Main Methods:

• A distributed event-triggered impulsive control strategy is designed.
• The approach incorporates Bernoulli stochastic variables to model random uncertainties.
• Matrix measure method and Lyapunov stability theorem are employed for analysis.
• Formula of variation of parameters and comparison principle are used for precise estimation.

Main Results:

• Sufficient conditions for achieving quasi-synchronization are derived.
• Convergence rate and synchronization error bound are precisely estimated.
• The proposed event-triggered function effectively eliminates Zeno behaviors.
• Numerical simulations validate the theoretical findings.

Conclusions:

• The novel event-triggered impulsive control effectively achieves quasi-synchronization in complex neural networks.
• The method provides robust control against time-varying delays and random uncertainties.
• The approach offers precise error bound estimation and avoids Zeno behavior, enhancing practical applicability.