Research On Information Spreading Models And Estimation Models Under Random Disturbance

With the development of the Internet,several kinds of social networks have sprung and become integral parts of our daily lives.Online social network provides a faster and freer platform to spread and exchange information while facilitate the diffusion of Internet rumors which have never been confirmed.Rumors may not only mislead people's judgements,affect the development of market economy,but also undermine the social stability.Therefore,it is of great significance to research the characteristics and regularity of rumor spreading dynamics on complex social networks.And then,the effective rumor spreading models and source estimation models would be established to research the rumor diffusion problem which has great significance in network security and public opinion monitoring.Classical rumor spreading models are based on epidemic models which are mainly deterministic in static networks.However,there exist several kinds of random perturbations during the rumor diffusion process such as the variation of connectivity among users which may change the network topology and the uncertainty of human behavior.As a result,we take the random perturbations into consideration which may help us realize the transmission mechanism more comprehensively.Four main contributions of the dissertation are as follows:(1)Considering the variation of connectivity,rumor spreading models on basis of stochastic differential equations(SDE)are established on both homogeneous and heterogeneous networks.We assume the variation of connectivity as noise which could be described as node degree modified with a standard Brownian motion.On homogeneous networks,we prove the existence and uniqueness of solution of the SDE model and derive the parameter condition of steady state that rumor will disappear in the network while time tends to infinity.Simulations on both artificial networks and actual networks display that the addition of noise accelerates rumor diffusion and expands diffusion scale,meanwhile,rumor spreads faster on heterogeneous networks than homogeneous networks under the same noise intensity.In addition,we find a positive correlation between peak value of the density of infected individuals and noise intensity while a negative correlation between rumor lifecycle and noise intensity overall.(2)Considering the uncertainty of human behavior,we model the rumor spreading process as a network game.Rumor diffusion in social networks is conducted by rational users,who would make strategic choices instead of being randomly infected with some probability.Due to the imperfection of background knowledge and the uncertainty in human behavior essentially,there exists random error while users estimate the benefits acquired from different choices which may change infection probability directly.Meanwhile,we also consider the random walk of rumor diffusion among different network distances with a spatio-temporal framework and propose a rumor spreading model based on partial differential equations.The global existence and uniqueness of solution has been proved with a Lyapunov function while the classical solution is also derived in format of infinite series.The iterative matrix of numerical solution has also been proposed through difference equations.Simulations display that density of infected users is dominated by network topology and uncertainty of behavior.With the increase of uncertainty,the density of infection in steady state increases firstly and then decreases which indicates that there exists the optimal uncertainty and stochastic resonance happens.(3)Based on the expectation of infection paths count,a two-source estimation has been proposed.And it is also applied to a kind of rumor tracing problem while exists an activation delay between two sources.We first discuss a single-source estimation in regular trees with a maximum likelihood estimation(MLE)to find the node which takes the maximum probability to be the source.While in two-source estimation problem,we simplify the problem into single-source estimation problem in two independent infection regions under determined partition.Through traversing all the possible partitions of infection regions,the distribution probability is calculated.As a result,the expectation of infection sequences count is treated as a new estimation.And then,we modify the distribution probability of partition to propose a heuristic algorithm which has also been promoted to general trees and general graphs.Detection accuracy of our estimation has also been verificated in both artificial networks and real networks.Compared with a kind of two-source estimation algorithm based on community division,our method performs better in tree-graphs and general graphs.Finally,the influence of activation delay on detection performance is also analysized and we conclude that an appropriate delay would construct a more accurate partition of infection regions and improve the detection performance within an error distance.(4)Focus on the dynamic network topology,an immunization strategy based on two-round selections is proposed.Network immunity aims at the key nodes which have great effect on diffusion process.And malignant information might be limited through controlling these nodes.However,classical immunization strategies are mainly on basis of static networks which may not be well applied in dynamic networks.We describe the dynamic network with a sequence of adjacent matrices and maximize the reduction of spectral radius of a system matrix.In the first-round selection,node degree,clustering coefficient and eccentricity are calculated to construct a screening node set while the final immune nodes would be selected with the reduction of spectral radius.The dynamic network is also approximated as an uncertain network which could be described with a probability graph model.The results show that the two-round selections based immunization strategy performs better in broking the connectivity of network and reduce the final scale of infected nodes in comparison with the strategy based on single central index under the same immune scale.