Weighted Networks And Dynamical Processes Of Complex Networks

The recent decade has witnessed the birth of a new movement ofinterest and research complex network. The researchers in physics,mathematics and computer all dedicate to the study of complex network.It's from the point of systematic view to study real systems, such as theInternet, power grid networks and telephone call networks, etc. In thisdissertation we study the modeling of weighted complex networks as wellas the dynamic properties of complex networks. These studies are veryimportant both in theory and in practical applications. Many real-worldnetworks are weighted networks with different weights in differentconnections. The unweighted network models studied in many existingliteratures are simplified modeling of real networks, while weightednetwork models can provide more realistic and comprehensivedescriptions of real networks. So, the importance of the modelling ofweighted networks is clearly self-evident. By studying the dynamicproperties of complex networks, on the one hand, we can understand andexplain the dynamic properties presented in real-world networks, such as,epidemic spread in network, synchronization and oscillation phenimena;and on the other hand, we can apply these theoretical results to somepractical applications. For example, we can apply these results to thedesign of real networks to achieve good performance or to the control ofreal networks to achieve some desirable network behaviors that benefit the networks.The thesis consists of four chapters. In chapter one, we introducedsome knowledge about network including the typical models of networkand the parameter to describe complex network. In chapter two, we studythe weighted network, at first we give a briefly review to the weightednetwork and some basic models of it. Then we put forward a new modelto generate weighted network. And we introduce some dynamicalprocesses on network in chapter three. Then at last we presents aconclusion for our work and some prospects for future works in this field.