Global synchronization in complex networks consisted of systems with the property of xkxk-leading asymptotic stability

Recently a large set of dynamical systems have been intensively investigated as models of complex networks in which there exist a class of very common systems with the property of xkxk-leading asymptotic stability [R. Zhang, M. Hu, Z. Xu, Phys. Lett. A 368 (2007) 276]. In this Letter, we introduced a new complex network model consisted of this systems, then considered its global synchronization. Based on Lasalle invariance principle, global synchronization criteria is derived. We also do not assume coupling matrix is symmetric and irreducible, so our model is more general than that of [R. Zhang, M. Hu, Z. Xu, Phys. Lett. A 368 (2007) 276]. What is more, our assumption f∈Quad∗(θ,P,α)f∈Quad∗(θ,P,α) is weaker than the assumption f∈Quad(D,P,α)f∈Quad(D,P,α) in [W. Lu, T. Chen, Physica D 213 (2006) 214], but it improves synchronization results greatly. Numerical simulations of Lorenz systems as the nodes are given to show the effectiveness of the proposed global asymptotic synchronization criteria.