Research On Opinion Dynamics For Friedkin-Johnsen Individuals In Cooperation-competition Networks

The opinion evolution of Friedkin-Johnsen individuals on the problem sequence is discussed for the cooperation-competition networks.Through theoretical analysis and numerical simulation,the convergence property of Friedkin-Johnsen individual opinion evolution on the problem sequence is obtained.The specific work is as follows:The first chapter introduces the research background and research status at home and abroad of multi-individual opinion dynamics evolution.The second chapter mainly introduces the concept of network topology,FriedkinJohnsen model and related theories and definitions.In the third chapter,we mainly discuss the opinion evolution of FriedkinJohnsen individuals in cooperation-competition networks under structurally unbalanced.In the research framework,the individual’s opinion dynamics is characterized by the Friedkin-Johnsen model,and the competition relationship between individuals is reflected by negative weights.It is worth noting that different individuals have different stubbornness,which indicates that the individuals considered are essentially heterogeneous.In order to solve the problem of the convergence of the individual point of view,the virtual individual is introduced by using the lifting approach,and the competition relationship in the original network is transformed into the cooperative relationship.The relationship between the original topology and the extended topology is established,and the sufficient conditions for the convergence of the individual on the problem sequence are given.Studies have shown that even if the weighted topology is structurally unbalanced,individual opinions can still achieve bipartite consistency under the influence of appropriate individual stubbornness.Finally,the correctness of the theoretical results is verified by numerical simulation.In the fourth chapter,we mainly study the opinion evolution of FriedkinJohnsen individuals in cooperation-competition networks in the sense of structurally balanced.It is worth noting that when the cooperation-competition network has a spanning tree and is structurally balanced,under the lifting approach,the extended topology can be decomposed into two independent spanning tree components.On the technical route,the viewpoint evolution problem of the total system can be transformed into the viewpoint evolution problem of a single spanning tree components.Furthermore,the relationship between the original topology and the extended topology is established by combining the individual stubbornness.By using the characteristics of the extended network topology and combining the individual stubbornness,a sufficient condition for the asymptotic convergence of individual opinions on the problem sequence is given.The research shows that when the network topology is strongly connected or only has a spanning tree and the FriedkinJohnsen model does not have a full stubborn individual,regardless of whether there is a non-stubborn individual,the individual opinion achieves bipartite consistency.Finally,the correctness of the theoretical results is verified by numerical simulation.The fifth chapter summarizes the full text and looks forward to the future evolution of individuals opinion.