Studies On Information Propagation Model Based On Mean Field Theory

With the development of complex network theory and its application in recent years,people begin to try to use this new theoretical tool to study all kinds of large and complex systems in the real world.For each network describing complex system,they each have their own uniqueness.The evolution of each network may be different,each network will have their own unique phenomenon.However,because they can be analyzed by the same network theory,they have something in common with each other.Statistical physics is an effective theoretical method to study this common characters.From the point of view of statistical physics,the network can describe the development of things or the relationship between the subsystems of the system as the interaction between nodes and nodes(edge),because the network itself is a system with a large number of interacting nodes.On this basis,the researchers will study more and more specific complex networks,which will be used in the theoretical and applied research of the network.Then,by discussing the specific phenomena occurring in the actual network,they explore a general way to model the phenomena occurring in the network,and then discuss the composition of the network itself and the laws it follows.Therefore,the use of statistical physics method can make the theory of complex network more powerful,so that the complex system of the real world gets more in-depth research.Social networks are one of the most rapidly growing real complex networks in recent years,both in terms of their own volume and types.The information itself and the connection between the users that it is expanded by the spread of information provides the source of power for the development of social networks.Users rely more and more on social networking sites because of the mass dissemination of various information on social networking sites,unfamiliar users will contact each other because of common attention on information;social networking sites will also become the main source of information for users,so information and social networking sites have an interdependent relationship.The research of information propagation,which involves physics,management,information science,biological information,preventive medicine and other disciplines,is a typical interdisciplinary research direction,and has received extensive attention in recent years.Generally speaking,empirical studies mostly start from the data and analyze the phenomenon of information explosion from the macro level;the dynamics study starts from the microcosmic level,understands the information propagation drive mechanism,mostly using SIR/SIS model disease model variant andso on;and the application research,from the point of view of the data or model fitting,expects to predict the results of the outbreak of information for corresponding public opinion prevention and control measures.The information propagation involves the many domains,also many application domains,like public opinion forecast,disease prevention & control,case inversion and so on.On the bases of mean filed theory and complex network theory,this dissertation studies the topological structure and statistical characteristics of online social networks,while in the course of research we appropriately apply the methods of statistical physics,and make empirical analysis and theoretical research on the laws of information propagation in actual online social networks.First of all,the process of information propagation in social networks is usually based on general model studies,such as SIR model,SIS model,SEIR model,or variants of these models to unify the description of information propagation.The form of these models is the first order nonlinear differential equations.First-order nonlinear differential equations are also widely used in mathematical modeling of many systems,such as physical systems,ecosystems,economic systems,social systems,etc.The general method of dealing with first-order nonlinear differential equations is qualitative analysis.There is no unified method for solving the exact analytical solutions of firstorder nonlinear differential equations.We analyze the general form of the first order nonlinear differential equations and obtain the exact analytic solution of a class of nonlinear differential equations in a complex system.Secondly,a series of information propagation models with the characteristics of population dynamics are established.The information propagation model with the characteristics of population dynamics is based on the following two properties of online social networks.First,online social networking is an open and complex system in which the total number of users is dynamic,not constant.Second,users in social networks have different level activities,that is,not all users in social networks will actively participate in the process of information propagation,only those active users will participate in the process of information propagation and evolution.The information propagation model with the characteristics of population dynamics takes into account the influence of the change of the total number of users and the degree of user activity on the information propagation.On this basis,the users who participate in the process of information propagation are classified,and the SIS model,SIR model and SEIR model with population dynamics characteristics are established.Thirdly,it collects data on Facebook's online social network with 4039 users.Statistical results show that online social networks such as Facebook have different network structures from small-world networks and scale-free networks.The basic topological features of the network,such as average path length,clustering coefficient and average degree,are different from small world networks and scale-free networks with the same number of nodes,but Facebook network still has small-world characteristics and its degree distribution satisfies the power-law distribution.On this basis,according to the degree distribution,clustering coefficient and other statistical characteristics of simple Facebook network with 4039 nodes,a generating algorithm suitable for Facebook network is obtained.Based on this algorithm,new nodes and edges are added to the simple Facebook network with 4039 nodes by networkx software,and an online social network with varying number of nodes is constructed.By using the information propagation model with population dynamics,we further study the process of information propagation on the network,and the numerical simulation results show that the information can be transmitted with oscillation in this network.The spread and evolution of rumors in social networks described by the information propagation model with the characteristics of population dynamics is different from the spread and evolution of rumors described by the previous information propagation model based on the warehouse infectious disease model.