Modeling,Source Identification,and Control Of Information Diffusion In Complex Networks

With the advent of globalization and the information age,people are connected through complex networks such as biological networks,transportation networks,and the Internet.The popularity of large online social network platforms has extensively promoted information sharing.The world’s accelerated connectivity has facilitated people’s daily lives,but the impact of various network diffusion risks is also increasing.There are various diffusion phenomena in nature and human society.The information diffusion problems on complex networks are based on these phenomena to model,analyze,predict,and formulate corresponding countermeasures for similar diffusion processes.It has been widely used in the research of epidemiology,information security,and public opinion guidance.Currently,most of the research mainly focuses on static networks,but more and more studies show that the entire complex network system is constantly changing.Hence,the accuracy and applicability of relevant studies are limited.To this end,according to the stochastic differential equation theory,graph theory,temporal network theory,stability analysis theory,and optimal control theory,this paper systematically studies information diffusion modeling,dissemination mechanism analysis,source identification,and information diffusion control based on the temporal network.The primary innovation consists of the following four parts:(1)A stochastic information diffusion model based on population noise and network connection noise is proposed to explore the impact of population size change and network topology change.Based on stochastic differential equation theory,we prove the existence and uniqueness of the positive global solution on homogeneous networks and derive sufficient conditions for the extinction of information.Numerical simulations are conducted on various networks to verify the theoretical analysis and evaluate the sensitivity of model parameters.The results show that the scale-free characteristics of the network and the increase of the basic reproduction number accelerate information diffusion,the introduction of network connection noise also accelerates information diffusion,and the population noise corresponding to infected individuals inhibits information diffusion.Besides,population noise plays a decisive role in information extinction when the noise intensity is large enough.(2)Single/multiple source identification estimators and corresponding algorithms are proposed to efficiently estimate the information sources and diffusion duration in temporal networks based on limited knowledge.The time-aggregated graph is introduced to record the connection relationship of the temporal network according to the temporal network theory.A reverse infection algorithm is developed to reduce the scope of seeking the source and ensure the feasibility of temporal path calculation.Resort to graph theory,the source estimator and single source estimation algorithm based on infection median are constructed.Subsequently,a multi-source estimation algorithm is designed to divide the infected node set and find the source in each partition.Meanwhile,we consider that the number of sources is a priori unknown.Simulation results on various temporal networks and the case study of rumor propagation verify the effectiveness of the proposed estimators and algorithms.(3)Two synergistic optimal control methods are proposed to suppress negative diffusion and enhance positive diffusion,which efficiently allocates control resources on temporal networks to achieve the desired goal.Considering the heterogeneity of individuals,we introduce continuous-time activity driven networks to refine the node characteristic.Based on the optimal control theory,the optimal control problem with different objectives is formulated.We prove the existence and uniqueness of the solution and obtain the optimal control signals.An implementation framework with a multi-layer hybrid feedback control scheme is developed for large-scale temporal networks.Diffusion parameters are accurately estimated and different control strategies are implemented using centralized and distributed techniques.Experimental results on empirical datasets verify the performance of the proposed synergistic optimal control methods and implementation framework.(4)Three synergistic control strategies are proposed to deal with negative information diffusion.The strong ties are introduced to explore the information diffusion control problem on static and temporal coupling networks.Based on the stability analysis theory,the critical threshold of the controlled system is derived.We formulate the resource allocation problems of budget constraint and risk constraint and provide the spectral optimization control scheme to minimize the outbreak risk or the required control resources.Through Pontryagin’s Principle,the optimal control scheme of dynamic and heterogeneous resource allocation is presented to minimize the cumulative cost of system losses and control expenses.Simulation results verify the accuracy of the theoretical derivation and the performance of the proposed control schemes.