Research On Minimizing Opinion Conlifcts Based On Friedkin-Johnsen Model With Pressure

The research on opinion dynamics has a practical significance for understanding,controlling and optimizing the real systems and also provides a unique perspective for understanding human's behavior patterns.The Friedkin-Johnsen model(referred to as F-J model for short)combines the properties of micro individuals with the emerging phenomena of macro groups,which has become a hot topic in recent years.F-J model has been widely used in different fields,but the assumption that the individual susceptibility to the group opinion remains constant is different from the results in sociological researches.Based on the research of F-J model,this thesis proposes a modified FJ model with pressure,which studies the influence of group pressure on the individual susceptibility,and reaches a consensus or a specific clustering by adjusting the convergence rate in the model as to minimize opinion conflicts in the networks.The main contributions are as follows:(1)According to the sociological descriptions of individual conformity-rejection characteristics under the group pressure,F-J model with pressure is proposed.In the F-J model with pressure,individual susceptibility is a state-dependent function of the difference of opinions between individual and groups,and an adjustable parameter convergence rate is introduced to adjust the susceptibility function.There is a critical convergence rate in the F-J model with pressure,which makes the network in the critical state between consensus and clustering.The relationship between the critical convergence rate and the structure convergence rate with the initial opinions distribution is studied through simulation experiments.(2)Opinion conflicts are defined as two parts: the external conflict of individual opinion contradiction and the internal conflict of individual opinion contradiction with real opinion.The optimization problem to minimize opinion conflicts in the network is defined.For the F-J model,the relationship between the final and initial opinion is expressed by the formal solution of the optimization problem and the network opinion evolution formula respectively,and a new convex optimization problem is solved to obtain the optimal susceptibility matrix that minimizes opinion conflicts.As for the F-J model with pressure,due to its state-dependent characteristics,the relationship between the final opinion and initial opinion is calculated according to its evolution mechanism,and listed as the constraint of the optimization problem,an algorithm to minimize opinion conflicts is proposed,and the optimal solution of the convergence rate vector is obtained.(3)When only some individuals are allowed to adjust susceptibilities in the network,this paper proposes a greedy algorithm to select the optimal target set for the F-J model,and an optimal target set selection algorithm based on measuring the difference between the final individual opinion and the target opinion for the F-J model with pressure.Compared with two common basic algorithms(F-J centrality and score algorithm),our algorithm significantly reduces network opinion conflicts in terms of optimization effect.