Pinning Impulsive Synchronization of Complex Dynamical Networks: A Stabilizing Delay Perspective

This brief investigates the stabilizing effect of delay in complex neural networks composed of homogeneous systems using pinning impulsive control. We focus on the limiting average impulsive interval (AII) and propose new conditions to establish the relationship between delay and convergence rate. It is shown that increasing delay within a specific range can lead to synchronization in initially desynchronized networks, resulting in faster convergence. We also determine the minimum control proportion required for achieving synchronization and provide insights into the relationships among control proportion, AII, and impulsive strength. The study highlights the importance of delay in network synchronization and presents a numerical example to illustrate its potential effects.