Adaptive feedback exponentially synchronization of complex delayed dynamical networks with nonlinearly coupled nodes

The paper investigates the adaptive globally exponentially synchronization of nonlinearly coupled complex dynamical networks with non-delayed and delayed coupling, which can reflect a more realistic dynamical behavior of coupled systems in practice. Based on Lyapunov stability theory, several novel adaptive globally exponentially synchronization criteria are obtained. Analytical results show that the states of dynamical networks can globally asymptotically synchronize to a desired orbit under the designed adaptive controllers. What is more, the coupling dynamic need not satisfy the very strong and conservative uniformly Lipschitz condition and the coupling matrix is not assumed to be symmetric or irreducible. Finally, a illustrate example with simulations is exploited to show the effectiveness of the theoretical results.