Research On Robustness And Disease Spread Of Complex Networks

We are surrounded by networks. Almost all of complex systems can be described in terms of complex networks. These networks contain many nodes and there are complex interactions among them. Along with the development of computerization of date acquisition led to the emergence of large databases on the topology of various real networks, it is found that many real networks have same features, such as small-world effect, scale-free property, degree-correlation and so on. These discoveries raise a new movement of interest and research in the study of complex networks. The problems on the evolution mechanism, dynamical processes, the relationship between the topological characteristics and performances on complex networks have recently received much attention. In this thesis, we investigate the attack robustness of network with duplication-divergence mechanism and controlling disease spread on networks with feedback mechanism. This study is believed to shed some light on the relationship of the topology and the dynamics. It can help us understand the behavior of network and improve the performance of network.The thesis consists of five chapters. In chapter one, we give a brief review to the history and the concepts of complex networks , then introduce briefly the statistical properties of complex networks. In chapter two, we introduce the properties of three kinds of typical network models. These models include the random network model (ER model), the small world network model (WS model) and the scale free network model(BA model). In chapter three, we study the attack robustness of network with duplication-divergence mechanism. We focus on the relationship betweenσand the networks' response to target attack qualitatively. Duplication-divergence network is broken down more quickly than its counterpart BA network under target attack. Such result is consistent with the fact of WWW and Internet networks under target attack. So duplication-divergence model is a more realistic one for us to investigate the characteristics of the world wide web in future probably. In chapter four, we study controlling disease spread on network with feedback mechanism. We have proposed a novel efficient feedback strategy for immunization. This strategy considers the networks' own adaptivity and the cost for immunization. After introducing the feedback mechanism, people tend to avoid contacts with infected individuals to protect themselves. It is shown that increasing the lethality a, the prevalence decreases more greatly with the same immunization g. That is, with the same cost, a better con- trolling result can be obtained. Besides epidemic dynamics, our findings also have strong implications for the spreading of information, opinions and beliefs in a population, which can be described in a similar way.