| Aiming at the influence network,studies the distributed evolution of social power of individuals with stubborn attributes.The specific work is as follows:The first chapter,from the perspective of sociology and control theory,introduces the opinion dynamics model and the evaluation mechanism of opinion evolution and the research status at home and abroad.The second chapter introduces the related theories and corresponding mathematical models(such as DeGroot model and Friedkin-Johnsen model)which are closely related to opinion dynamics and evolution research,and expounds the lifting method in cooperative competition network.The third chapter discusses a series of problems about the evolution of social power of stubborn individuals in the cooperative competition network.In the research framework,the evolution of individuals’ opinions is described by the FriedkinJohnsen model.It is worth noting that the stubborn attributes of individuals in this model are characterized by the persistence of individuals’ initial opinions,and affect both cooperative and competitive relationships among individuals in the network.Due to the introduction of competitive relationship,the relative interaction matrix has negative weights.Therefore,the lifting method is used to add virtual individuals and then convert the original competitive relationship into a cooperative relationship between individuals and virtual individuals.For the case that the original cooperative competition network is strongly connected and the structure is unbalanced,the relationship between the original cooperative competition network and the cooperative network under the action of the lifting method is established.Further,according to the reflection evaluation mechanism,the mathematical model of the distributed evolution of individual social power in the cooperative competition network can be obtained.Based on this model,the existence,uniqueness and convergence conditions of the corresponding balanced social power are obtained by using Banach fixed point theorem.The results show that the convergence is related to the network topology and the individual’s stubbornness.Further,for the case where two individuals are given the same influence weight by partial stubborn individuals,the more stubborn individuals have greater balance of social power.In addition,we also consider the evolution of individual social power under two special topologies,namely star network topology and ’double random’ network topology.Finally,numerical simulations are provided to verify the correctness of the relevant theoretical results.The fourth chapter proposes a mathematical model based on the interval reflection evaluation mechanism and studies its distributed evolution of social power in the cooperative influence network.It is worth noting that the formation of opinions and the evolution of social power are carried out at the same time scale,that is,the single time scale mathematical model.In this mathematical model,the evolution of opinions is still described by the Friedkin-Johnsen model,and the self-weighting vector is updated step by step.In the technical route,the matrix vectorization method is used to convert the original system into a nonlinear mapping.The existence of the equilibrium point of the system is obtained by schauder fixed point theorem,and then the conditions of uniqueness and convergence of the corresponding equilibrium social power are obtained by the compressibility analysis of nonlinear mapping,the results show that convergence only depends on individual susceptibility.Finally,numerical simulations are provided to verify the correctness of the theoretical results.The fifth chapter summarizes the full text and looks forward to future research directions. |
