Outer Synchronization And Mixed Outer Synchronization Of Two Delay Complex Networks

Synchronization, which means that a typical kind of collective dynamics behavior in complex network, has attracted considerable attention from different subjects of researchers in recent years. Mainly because that it often occurred in the real network.As we know that the investigation of synchronization in the complex network need the knowledge of the differential dynamics, the network theory, the stability theory and so on,which has great challenge. While a mass of researches only study the synchronization of the nodes in one network system(usually called inner synchronization), the investigation of synchronization between the two different network system(which called outer synchronization) has much more theoretical signi?cance and application value. In this academic dissertation, we mainly study the outer synchronization and the hybrid outer synchronization of the complex network with time-varying delayed. Our main work includes the following several aspects:In the second chapter, we give some preliminaries such as the de?nition of outer synchronization, lemmas that are necessary throughout the paper, and some notations.We get the differential inequality with time-varying delay, which extend the piecewise continuously differentiable delay differential inequality in the available literature, and it will be the essential tools to study the outer synchronization of the network with timevarying delayed via impulsive control.Next, we will use two kinds of control strategies to investigate the outer synchronization of two complex networks with non-delay coupling and time-varying coupling.The ?rst and foremost, we give the negative linear feedback control to some nodes in the response network, according to the Lyapunov-Krasovskii Stability Theorem and the Linear Matrix Inequality, we derive some su?cient conditions of the outer synchronization. There is one more point, we give impulsive control to a portion of the nodes in the network, some su?cient conditions for the outer synchronization are obtained based on the extend differential inequality. And we compared this with the existing research results.In the fourth chapter, we study the mixed outer synchronization of the two complex networks with special node dynamics and time-varying delayed coupling. Using pinning control strategy, the mixed outer synchronization of the two networks is achieved by designing a special kind of controller. Similarly, impulsive control are given to the nodes of the response network, we obtain the mixed outer synchronization of the drive network and the response network, the main result generalize the existing conclusions.In this paper, all of the theoretical results have been veri?ed by actual numerical example.