Impulsive Effects on Quasi-Synchronization of Neural Networks With Parameter Mismatches and Time-Varying Delay

Area of Science:

• Control Theory
• Computational Neuroscience
• Network Dynamics

Background:

• Neural networks often exhibit parameter mismatches, hindering perfect synchronization.
• Time-varying delays introduce complexity in analyzing network behavior.
• Quasi-synchronization, a weaker form of synchronization, is relevant for practical applications.

Purpose of the Study:

• To investigate the exponential quasi-synchronization of nonidentically coupled neural networks with time-varying delays.
• To develop and analyze impulsive control strategies for achieving quasi-synchronization.
• To explore the dual role of impulsive effects (beneficial or detrimental) on network synchronization.

Main Methods:

• Application of impulsive control strategies.
• Utilizing the definition of average impulsive interval.
• Employing the extended comparison principle for impulsive systems.
• Derivation of criteria for quasi-synchronization based on theoretical analysis.

Main Results:

• Criteria for achieving quasi-synchronization of neural networks are derived.
• Analysis covers extensive ranges of impulsive effects, including adverse roles.
• Precise exponential convergence rates and quasi-synchronization errors are obtained.
• Numerical simulations validate the theoretical findings for various impulsive effects.

Conclusions:

• The proposed impulsive control strategies effectively achieve quasi-synchronization in nonidentically coupled neural networks with time-varying delays.
• The study provides a comprehensive analysis of how impulsive effects influence network synchronization.
• The derived criteria and methods offer a robust framework for understanding and controlling complex neural network dynamics.