Analysis And Control Of Propagation Dynamics Based On Complex Networks

Research based on complex network propagation dynamics is a key issue in the theory and application of complex systems.Its research has great relevance to the development of big data and artificial intelligence.The research on the propagation dynamics of complex networks can be roughly divided into two major directions: databased and model-based,according to the above two aspects.This paper mainly analyzes and controls the propagation process on the complex network based on the diffusion model.In recent years,the propagation models established for the complex network in real life are emerging one after another,but there is still no unified modeling method to describe the complex propagation process in reality.In this paper,a dynamical model containing network topology information is established based on the theory of differential equation,and the corresponding intervention mechanism is designed for latent virus transmission,and the optimal control problems under the background of public opinion and epidemic transmission are discussed.First of all,based on the incubation characteristics of viruses,the use of Nintertwined mean field approximation method is taken to establish the SNIS(susceptibleincubated-infected-susceptible)delay propagation model.For the latent individuals,two intervention strategies are proposed: continuous detection strategy and impulsive detection strategy.In this paper,the stability of the disease-free equilibrium point of the delay propagation system with the detection mechanism is strictly proved by using relevant theories and inequalities,and the sufficient conditions that should be satisfied when the two strategies can effectively inhibit the virus transmission are given.Secondly,an individual-based SEIS(susceptible-exposed-infected-susceptible)distributed delay propagation model is established for the non-uniform latency caused by individual differences,which also contains the structural information of the network.In this paper,the propagation behavior of information in the network after the time of maximum latency is analyzed,the local global asymptotic stability of the disease-free equilibrium point of the system model is analyzed,sufficient conditions for the persistence of virus information in the system are given,the local equilibrium point of the model is obtained,and the local global stability of the equilibrium point is discussed.Studies have shown that,regardless of the consistency latency or the non-consistency latency,the shorter the cycle,the better the virus’ s demise in the network.Thirdly,based on the network individual model SIRS(susceptible-exposedrecovered-susceptible),the external control effect of infection rate and removal rate is proposed.By means of Jacobian matrix,the error system corresponding to the propagation model is analyzed,and the stability of the disease-free equilibrium point under the control of the model is proved.The sufficiency condition that control should be satisfied when it dies in the network.Next,based on the above SIRS model,two types of optimization problems are proposed,namely,how to maximize the coverage of the final state of the transmitted information and how to minimize the overall infection level of the network during the whole transmission process.Finally,the main research contents of this paper are summarized and the future research directions are prospected.