Dynamic Analysis Of Network Rumor Propagation Model

In the network era,the efficiency,speed and universality of information dissemination have been greatly improved,and at the same time,it has also contributed to the breeding and dissemination of rumors.The spread of online rumors breaks through the restrictions of crowd and space and time.The rumor disseminators are not only interactive,but also their number will increase in geometric progression,which is difficult to estimate.Therefore,it is of great significance to study the dynamics of rumor propagation to reduce false news and ensure the authenticity of news information.Based on the classical rumor propagation model and the characteristics of rumor propagation,this thesis studies the dynamic characteristics of rumor systems by using the theory of differential equation.The main work is as follows:1.Based on the classic SI rumor propagation model,a rumor propagation model with psychological adjustment factor and double time delay is studied.First,the existence of equilibrium point is verified;The basic reproduction number of rumor propagation is calculated by spectral radius method.Secondly,the local stability of the boundary equilibrium point is judged by the characteristic root of the characteristic equation of the linear system.Furthermore,the local stability of the positive equilibrium and the conditions for the occurrence of Hopf bifurcation in different delay states are given.Finally,the reliability of the theory is verified by simulating the local stability of the positive equilibrium point.2.A SI reaction-diffusion rumor propagation model with nonlinear saturation incidence is studied.Firstly,through stability analysis,we obtain the conditions for the existence and local stability of positive equilibrium.Select variable μ as the control parameter,the critical value of Turing bifurcation and the existence theorem of Turing bifurcation are obtained.Then,using the above theorem and standard multi-scale analysis method,the amplitude equation near the critical value of Turing bifurcation is derived.By analyzing the amplitude equation,different types of Turing pattern are divided,such as uniform steady-state mode,hexagonal mode,stripe mode and mixed structure mode.Further,in the numerical simulation part,by observing different patterns corresponding to different values of variable μ,the correctness of the theory is verified.Finally,the effects of different network structures on patterns are investigated.The results show that the density distribution of each population is inconsistent on WS network(Watts-Strogatz network)and BA network(Barabasi-Albert network).3.A reaction-diffusion dynamic model with time delay is established under the background of network rumors,and the behavior of susceptible users and infected users in spreading rumors on the network is analyzed to help us study the mechanism of rumor propagation to manage public opinion.Firstly,the Turing instability condition of delay approximate system is studied.Secondly,based on the amplitude equation method,the theoretical conditions of different patterns near Turing bifurcation point are given,and different types of Turing patterns are divided.Then,the accuracy of the theory is verified by numerical simulation under different parameters,and the effectiveness of the model is verified by Monte Carlo simulation.In addition,the effects of different networks and time-delay conditions on pattern formation are studied.Finally,in order to help the model apply to the actual situation,the parameter identification and optimization control of the system are carried out.