Synchronization of multi-weighted complex networks with mixed variable delays and uncertainties via impulsive pinning control

Abstract

In this paper, the synchronization problem in nonlinearly-coupled multi-weighted complex networks with parameter uncertainties and multiple delays, where both internal time-varying delays and multiple coupling time-varying delays are included, is investigated by adopting a pinning impulsive control scheme, which combines the merits of pinning control and impulsive control. Impulsive pinning control ratio has been applied to select controlled nodes at each impulsive instant. Based on the Lyapunov function method, sufficient conditions for achieving complete synchronization of multi-weighted complex networks have been derived. And numerical simulations are presented to demonstrate the validity and efficacy of our derived theoretical results, which show that under the criteria proposed in this paper, multi-weighted complex networks with parameter uncertainties and multiple delays, could achieve complete synchronization by applying pinning impulsive control. Besides, taking bus lines as the network nodes, a public traffic roads network model with multi-weights is established and analyzed numerically as an application of the proposed multi-weighted complex network model.