Synchronization Of Directed Complex Dynamical Networks Based On Event-triggered Communications

A complex dynamic network is closely related to modern daily life. Synchronization is one of the most important cluster behavior of complex dynamic network. In laser systems, superconducting material and communication systems, synchronous behavior plays an important role. Due to the dynamic behavior of chaotic systems is ideal, in the study of synchronous phenomenon of complex network, people often use chaotic system instead of independent nodes. In addition, the network in the real world is very complex. And the topological structure of network is not necessarily symmetrical. Generally, the exchange of information is in accordance with the continuous of discrete time in a complex network. In this paper, the proposed event-triggered mechanism determines in accordance with what frequency the nodes send status information. Under this kind of trigger mechanism, the complex network avoids the unnecessary communication. Based on the Lyapunov stability theory and the design of the event-triggered mechanism, data sending criterion is given in this paper.The main contents are as follows:Firstly, using Lyapunov stability theory, the centralized and distributed event-triggered mechanism is designed to the directed complex dynamic network. And the complex dynamic network achieves synchronization under the event-trigger. Then the numerical simulations are provided to demonstrate the effectiveness of the proposed event-triggered mechanism.Secondly, for the directed complex dynamic network, using Lyapunov-krasovskii theory and the analysis of the method of time delay system, the event-triggered mechanism and the synchronous rule are given. The numerical simulations are provided to demonstrate the effectiveness of the proposed event-triggered mechanism and synchronous rule.Finally, there is some external disturbance in the directed complex network. In this case, the design of event-triggered mechanism and synchronous condition are considered. This research adopts the theory of Lyapunov-Krasovskii function and H_∞ control theory. The numerical simulations demonstrate the effectiveness of the proposed event-triggered mechanism and synchronous rule under the external disturbance.