Opinion Dynamics Models With Multiple Interdependencies

With the development of science and the progress of communication technology,the way of information interaction between individuals has undergone great changes,and the amount of information obtained is increasing day by day.In this case,individuals often interact with opinions on multiple topics,rather than on a specific topic.This not only increases the amount of information in social networks,but also makes the connection between individuals and the way of information exchange more complicated.Therefore,it is of great practical significance to consider the interaction of opinions among individuals on multiple interdependent topics.In this thesis,we mainly study how heterogeneous logical interdependence between topics affect the evolution of opinions,and also consider the influence of competition mechanism,switching topology and stubborn individuals on the evolution of opinions.The main contribution of this thesis can be listed as follows:(1)Based on the classic De Groot(DG)model,we propose an opinion dynamics model with antagonistic(competitive)relation and multiple interdependent topics under switched topology.This model aims to characterize the evolution of individual opinions when individuals in a signed social network are able to discuss multiple interdependent topics simultaneously.Considering that different individuals may have different perceptions of the same thing,a set of heterogeneous logical matrices is used to represent the logic interdependence between different topics.We consider structurally balanced networks and structurally unbalanced networks respectively.By using the method of matrix analysis,some sufficient conditions for the modulus consensus about topics are obtained in our study.After that,we verify the effectiveness of the conclusions through several examples.(2)Based on the classical Friedkin-Johnsen(F-J)model,we propose an opinion dynamics model with stubborn individuals,competitive relationships and multiple interdependent topics.In particular,the interdependence between topics is heterogeneous.We rigorously concentrate on its convergence and stability for the structurally balanced and unbalanced social networks.And some conditions on the convergence and stability are obtained.All the obtained conditions depend on the network topology and logical matrices and fully show how the network topology and logical matrix influence the evolution of opinions.Finally,several examples are used to verify our results.At the end of this thesis,we summarize the work of this thesis,and look forward to the future research direction of opinion dynamics.The relevant research results of this thesis have certain practical significance for promoting the development of opinion dynamics,enriching the connotation of individual belief system,and revealing the evolution law of opinion generation,diffusion and aggregation.