Synchronization in Coupled Neural Networks With Hybrid Delayed Impulses: Average Impulsive Delay-Gain Method.

Area of Science:

• Neuroscience
• Control Theory
• Network Science

Background:

• Coupled Neural Networks (CNNs) are fundamental to understanding complex brain functions.
• Synchronization in CNNs is crucial for information processing but challenging due to delayed impulses.
• Existing methods often lack flexibility in handling time-varying parameters.

Purpose of the Study:

• To introduce a new metric, average impulsive delay-gain (AIDG), for analyzing CNN synchronization.
• To develop novel, less conservative synchronization criteria for CNNs with hybrid delayed impulses.
• To investigate the dual (positive and negative) effects of AIDG on network synchronization.

Main Methods:

• Development of novel globally exponential synchronization criteria.
• Analysis based on impulsive control and impulsive perturbation theory.
• Application of the Average Impulsive Delay-Gain (AIDG) concept.

Main Results:

• Established new synchronization criteria applicable to hybrid delayed impulses with time-varying delays and gains.
• Demonstrated that AIDG can both facilitate and hinder synchronization.
• Showcased the flexibility and reduced conservatism of the proposed methods.

Conclusions:

• The AIDG concept provides a more comprehensive framework for CNN synchronization analysis.
• The derived criteria are more broadly applicable than existing methods.
• The findings were validated on small-world and scale-free network models.