| The spread of viruses, informations, rumors and public opinions based on social networksalso permeate our social, economy, politics and military. In the military field, once thecomputer virus invades the military network, it can leak the military intelligence and interruptthe transmission of the network information. In the political field, the propagation of crisisinformations and political opinions can bring serious impacts on the security and stability ofour nation. In our daily lives, the diffusion of rumors and the propagation of virus can affectpeople’s physical and mental health. These propagations are related with not onlycharacteristics of propagations but also network topology. Different network structures havedifferent effects on the scale and the threshold of propagations and control strategies. Thus,studying the topology structure of networks and the dynamic characteristics of variouspropagations on the network is undoubtedly an important issue of studying the dynamics ofcomplex networks, it can provide the theorectical support and methodological guidance forthe propagation. To this end, combining the explicit patterns of contacts and statisticscharacteristics, we describe the topology structure of several specific social networks.Considering different propagation mechanisms, we propose some dynamical models on thenetwork and discuss their dynamical behaviors using the method of mean-field and thepercolation theory. Some threshold conditions are obtained, and some propagations measuresare provided. The detailed contents are as follows:In chapter2, an introduction about some basic theories of complex networks and someresearch methods of propagation on the network are given. The specific contents includesome basic concepts about the network, the characterization of topological structures and thedescription of evolution mechanisms and statistical properties of four classical networks, inaddition, two research methods about network propagation are given.In chapter3, based on the interpersonal contacts in the process of new products diffusion,we present a heterogeneous network model with the awareness stage and the decision-making stage to explain the process of new products diffusion. If mass media is neglected orconsidered in the decision-making stage, in the regular and heterogeneous networkrespectively, the condition whether the innovation diffusion is successful or not is discussed,the influence of degrees of the buyers on product diffusion is studied.In chapter4, considering the transmission heterogeneity of different types of edges(linesand edges in the triangle), we formulate and analyze a novel SIS model on the network withcluster based on the network mean-field approach. We mainly focus on how networkclustering influences the network structure and the virus spread.In chapter5, we consider an interconnected network with two layers. The network in eachlayer describes the intra-layer transmission of the virus, the network between two layersdescribes the inter-layer transmission of the virus. We assume there are the intra-layertransmission and the inter-layer transmission of the virus, and double degrees which describethe numbers of intra-layer contacts and inter-layer contacts are introduced, correlationcoefficients about degrees based on the joint probability distribution are given, and an SISmean-field model on the interconnected network is presented when degrees are uncorrelated.The basic reproduction number of the transmission is studied by the method of nextgeneration matrix. The epidemic relations of the virus among every subneworks and thewhole network are studied.In chapter6, using the percolation theory, we study an SIR model on an interconnectednetwork. By the method of the probability generating function, we discuss the conditionwhether the virus is epidemic or not and the average size of outbreaks when there is noepidemic. We also discuss the risk factor which the virus is epidemic and the infection size isincreasing. |
