Synchronization for Directed Multi-Level Complex Networks With Multiple Weights
Leijing Xie, Xiwei Liu
Abstract
In this paper, we study the synchronization problem of directed multi-level complex networks (MLevelN). Firstly, directed multi-layer complex networks with multiple weights are successfully transformed to directed multi-layer complex networks with a single weight by using the newly developed re-arranging variables’ order technique. Moreover, as a typical representative of the MLevelN model, we propose some novel Lyapunov functions by the Kronecker product of the left eigenvectors for multi-layer networks, and we also illustrate the processing procedure can be simply extended to more complicated MLevelN. Furthermore, the pinning control strategies for various synchronization types are also designed with constant and adaptive strengths respectively. The obtained criteria can greatly improve the conservation of previous works, whose effectiveness is demonstrated by numerical simulations.