Synchronization of Multi-Weighted Complex Networks with Mixed Variable Delays and Uncertainties Via Impulsive Pinning Control

Abstract

In this paper, we examine the synchronization problem in nonlinearly-coupled multi-weighted complex networks that contain uncertainties and varying delays. The complexities of these networks arise from the presence of both internal time-varying delays and multiple coupling time-varying delays. To address this challenge, we employ impulsive pinning control schemes and incorporate the impulsive pinning control ratio in the construction of the Lyapunov function, which allows us to determine the optimal number of pinned nodes at each pulse instant. Our analysis, based on stability theory, provides synchronization criteria that are strongly dependent on the multi-weights and time delays present in the network. Finally, we present numerical simulations of a delayed complex network to demonstrate the validity and efficacy of our derived theoretical results.

Keywords: complex network, synchronization, Impulsive pinning control, Uncertainty, Multi-weighted.