Global synchronization for directed complex networks

Synchronization for generic directed networks is investigated in this paper. Based on Lyapunov stability theory, a sufficient condition for synchronization of directed networks is derived. Compared with other approaches, where weighted path-lengths are required, or the complex eigenvalues of an asymmetric matrix, Jacobian matrix or Kronecker product need to be calculated, the sufficient condition in this paper is simple and convenient to use. Two typical examples of directed networks with chaotic nodes are finally demonstrated to verify the theoretical results and the effectiveness of the proposed synchronization scheme.