Pinning control of spatially and temporally complex dynamical networks with time-varying delays

In the present paper, two types of complex delayed dynamical networks with spatially and temporally varying state variables are proposed. The first is that all nodes in the network have the same time-varying delay. The second is that different nodes have different time-varying delays. We respectively investigate the stabilization problem of these two types of complex network models by pinning a small fraction of nodes with negative feedback controllers. With the help of Lyapunov functionals and some inequality techniques, several asymptotic stability and exponential stability conditions are established. Finally, numerical simulations are presented to illustrate the effectiveness of the results obtained here.