Synchronization of Time-Delay Coupled Neural Networks With Stabilizing Delayed Impulsive Control

Area of Science:

• Control Theory
• Computational Neuroscience
• Network Science

Background:

• Distributed synchronization is crucial for coupled neural networks (NNs).
• Time delays and impulsive control present challenges in achieving synchronization.
• Existing methods often have limitations on delay parameters.

Purpose of the Study:

• To investigate distributed synchronization of time-delay coupled NNs with impulsive pinning control.
• To develop novel methods for handling stabilizing delays in such systems.
• To relax existing constraints on impulsive delays and improve synchronization criteria.

Main Methods:

• A novel differential inequality is proposed to utilize past information at impulsive times.
• The average impulsive interval (AII) and impulsive delay methods are employed.
• Synchronization criteria are derived by analyzing the system's dynamics under impulsive control.

Main Results:

• A new inequality effectively extracts and uses state information at impulsive times.
• The restriction of impulsive delay being less than system delay is removed.
• Relaxed criteria for distributed synchronization are obtained, improving existing results.
• Impulsive delays are shown to potentially aid synchronization.

Conclusions:

• The proposed impulsive pinning control method offers improved and more flexible synchronization criteria for time-delay coupled NNs.
• The findings demonstrate that carefully designed impulsive delays can be beneficial for system synchronization.
• The study validates the effectiveness of the delayed impulsive control approach through network simulations.