| The complex network exists widely in nature and human society, such as nets of the relationships, the technology's papers nets, the World Wide Web etc. These networks demonstrate the more complex topological properties. As the small world's features of the network and scale-free characteristic are discovered, the complex networks have attracted many scholars'attention. It is got centralized embodiment in the aspects of network dynamics analysis, network modeling and computing applications. Among these synchronous characteristics is one of the most popular topics on the complex network. In the real life, the synchronous phenomenon is influence widely on the modern society at the same time. Something such that frogs scream together and fireflies flash consistently and so forth In the realistic society, it has practical significance broadly to research on synchronous; we can make full use of the useful synchronization, such as security communication, the generated harmonic oscillator, the coordination of organization and management and efficient operation, etc. Of course, harmful synchronization should be avoided, for example, information jams of the communications networks, router's synchronization etc.In the first section, The synchronization is analyzed and studied among the complex dynamic delay network. Firstly the concept of the complex dynamic delay network has been proposed. Then some sufficient conditions on synchronization of the system are presented by Lyapunov functional and LMI method.In the second section, the nature of the synchronization output of the complex networks including the dynamic delay has been analyzed Firstly, it is established that mathematical model with output of complex dynamic and coupled delay network, including different time-varying and time-delay of the nodes'state. The criterion of the synchronization output is obtained by constructing Lyapunov functional, and by using the linear matrix inequality (LMI).
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