Research On Opinion Dynamics Based On Q-voter Model And Concealed-voter Model

To reach consensus and make decision is one of the basic activities of human soci-ety,and the main research content of opinion dynamics.Whether group consensus can be reached and the time it takes to achive consensus is affected by which factors are the research topics of opinion dynamics.The researchers have proposed many opinion dy-namics models to study the evolution of group opinions in order to accurately describe and predict the process of opinion formation.The research results of opinion dynamics are widely used in many life scenes,such as political election,marketing,transportation,public opinion management and so on,which brings convenience to our life.Although there are many opinion dynamics models,most of these models are too idealized.Later researchers enriched the research contents of opinion dynamics from different angles through extended research.In general,researchers mainly do innovative research in the following two directions: first,put forward a more realistic opinion dynamics model?second,through the expansion of the original model to do further research.In this the-sis,the phase transition phenomenon and the consensus time problem are studied by expanding the original q-voter model and the concealed-voter model(CVM),respec-tively.In the first part of the thesis,the study on phase transition phenomenon in mutistate q-voter models driven by independence are introduced.Phase transition phenomenon is one of the research contents of opinion dynamics.The researchers studied phase transition by incorporating anticonformity and independence into the opinion dynamics models.In chapter three,we extend the twostate q-voter model to the multistate q-voter model and introduce independence into the model to study the phase transition behavior in the extened model.We have calculated order parameters,fluctuation of order parameters and Binder cumulant with noise intensity by a large number of Monte Carlo simulations.The results show that the dynamic process only occurs discontinuous phase transition.Previous studies have shown that in the twostate q-voter model driven by independence the phase transition type of the dynamics changes from continuous phase transition to discontinuous phase transition with the increase of q.This result shows that the number of opinion states also affects the opinion dynamics when the opinion update rule is the same.In the second part of the thesis,the study on the consensus time of a concealed-voter model with individual heterogeneity are introduced.Among the extened opinion models,concealed voter model is a recently proposed classic model that considers both public and private opinions,which can be simply described as: everyone on the network has two opinions,in which one is publicly expressed and the other is deep inside.The following three independent processes occur in the evolution of the system: with the rate c the external opinions is update according to the voter model update rules(copying)?the external opinion becomes the internal opinion with the rate i(internalization)? the internal opinion becomes the external one with the rate e(externalization).There will be no direct exchange of opinions between internal opinions.However,three parameters c,e,i in the original CVM is the same for every individual,which ignores individual's differences in reality.In chapter four,we let the three parameters c,e,i of the CVM obey the power law distribution.After this improve,we call the model heterogeneous concealed-voter model(HCVM).Applying the heterogeneous mean-field approach and backward Kolmogorov equation to HCVM,we analytically calculate the consensus time and exit probability on fully-connected networks and find the conservation law that dominates the dynamics.By comparing the results of CVM and HCVM,we find that the heterogeneity of copying rate c and internalization rate i can delay the formation of consensus state,while the heterogeneity of externalization rate e can accelerate the formation of consensus state but slightly.Finally,the analytical results are validated by a large number of computer simulations.