Dynamics Of Complex Network With Feedback Mechanism

Complex network can be tangible objects in the Euclidean space, such as electric power grids, the Internet, highways or subway systems, and the neural network. In recent years, the analysis and modeling of networks, and also networked dynamical systems, have been the subject of considerable interdisciplinary interest, yielding several significant works in physics, mathematics, computer science, biology, economics, and sociology. It is now known that the dynamics of complex network is very crucial to the research of it.In this dissertation, firstly, we introduce a feedback mechanism to study the spreading of an epidemic by analytical methods and large scale simulations in exponential networks. It is found that introducing the feedback mechanism can reduce the density of infected individuals. Furthermore, it does not change the epidemic threshold. These results can help us to understand epidemic spreading phenomena on social networks more practically and design appropriate strategies to control social infections. Secondly, based on the Ising spin system and the Sznajd model (SM), we introduce a new model to study the opinion evolving in SM on square lattices by large scale numerical simulations. To be more realistic, two basic impacts are considered in the process of the eight individuals' decision-making, i.e., the information governed by the neighbors and the average opinion of the whole community. It is found that our model show many useful and interesting statistical results.The thesis is organized as follows:In chapter 1, we give a brief review to the study of complex networks, including it's background main contents and significance.Chapter 2 is about the basic concept of the graph and parameters of the complex networks. We then briefly review the main models that have been proposed over the years, focusing on random graphs, small-world models, scale-free networks and hierarchical networks. Finally, we give a special emphasis to the study of dynamics and synchronization in complex networks.In chapter 3, we review two classical models of spreading of epidemics and three important strategies of immunity. Then we consider the epidemic dynamics with feedback mechanism in exponential networks.In chapter 4, we analyze the opinion formation in Sznajd model with more complex social impact.Finally, chapter 5 summarizes our main work during the Master and presents outlooks of future works in this field.