Abstract:

Based on current complex network models, a new and general double-linked complex network with time-varying delayed nodes and couplings was introduced. This model not only contains two sub-networks of different natures but also delayed nodes and couplings, and the two types of delays are both time-varying. Via the Lyapunov-Krasovskii functional method, under smaller conservative assumption and weaker requirements of the network parameters, the adaptive feedback controllers of the complex network for asymptotic synchronization and exponential synchronization were designed by using inequality. The results of numerical calculation show the effectiveness of the control methods. By giving the same initial value, it is verified that the synchronous speed of the network under exponentially synchronous control is faster.

Key words:  complex networks, exponential synchronization, Lyapunov-Krasovskii function, adaptive feedback control