The Study Of Spreading Dynamic On Complex Networks

It is now universally acknowledged that complex network is a novel and efficient tool for characterizing and studying various complex structures in both nature and society. Recent years have witnessed great advancement in this active field of statistical physics. Complex networks created by some typical models replace the random graphs and provide more accurate description for the real complex systems. Naturally, the functions and dynamical processes on complex systems becomes a new research branch in the field of complex networks. Study of spreading dynamics on complex networks, as a subject filling with physical principles and methods, has received a lot of attention from various disciplines such as physics, sociology, computer science and so on. These studies are of great significance in the understanding of spreading behaviors of various virus, information and things in complex systems, and then for exploring the ways to control the behaviors. So far, the study of the spreading dynamics and the corresponding controlling strategy on complex networks has been in its infancy, since knowledge of the topology and dynamic of complex networks is insufficient. In this thesis, based on the traditional epidemic spreading models, we systematically study the epidemic spreading, including spreading threshold, microscopic infectious mechanism and the controlling strategy. We also propose two immunization strategies by virtue of random walks, where only local information of networks'connectivity is needed. The thesis consists of five chapters. In chapter one, we give a brief review to the study of complex network and then introduce main content of this thesis. In chapter two, we introduce briefly some basic concepts about complex networks. In addition, some statistical properties of real networks and their corresponding network models together with several dynamical processes taking placing on complex networks are presented. In chapter three, three kinds of classical spreading models are reviewed. Based on these models, we systematically introduce the dynamical behaviors of the epidemic spreading. In this chapter, we also systematically study the finite-size effects of the thresholds, where some valuable results are...