Coevolutionary Analysis Of Individual Perspectives And Social Power In The FJ Model With Forgetful Individuals

As an important carrier of the evolution of individual perspectives and social power,opinion dynamics,as a cutting-edge discipline in the field of control,is attracting the attention of researchers from different scientific fields.The core of the evolution of in-dividual viewpoints and social power in the opinion dynamics lies in the individual’s own social psychology and the topology of influence weight networks among individuals.Therefore,it is of important research significance and application prospects to analyze the co evolution trend of individual viewpoints and social forces by setting a series of indi-vidual social psychological characteristics and influence weight networks.Using graph theory,matrix theory,and other analytical methods,this thesis studies the co evolution of individual perspectives and social power in the FJ model with forgetful individuals,and explores the characteristics of the evolution of individual viewpoints and social power evolution on this basis.The specific research work is as follows:The first chapter describes the development and current research results of the dy-namics of individual viewpoints and the evolution of social forces,and presents the sig-nificance of the study of individual viewpoints with forgetfulness and the evolution of social forces,leading to the main research work of this article.The second chapter introduces the relevant theoretical knowledge in algebraic graph theory and matrix theory involved in this study,including the definitions of cooperative competitive networks and structural equilibrium and non equilibrium,row random matrix,strongly connected network topology,and Perron-Frobenius theorem and Schauder fixed point theorem,and provides symbolic explanations related to this article.Chapter 3 studies the evolution of individual social power in the FJ model with for-getful individuals.The dynamic equation for the evolution of individual social power is represented by modeling an FJ model with forgetful individuals.For the evolution of social power with forgetful individuals,this chapter uses path dependence theory to propose a well posed condition for the evolution of individual social power in this sit-uation.Furthermore,based on this condition and the Schauder fixed point theorem and the Perron-Frobenius theorem,the existence of an equilibrium point for the evolution of social power is proved,Using matrix norm theory,the uniqueness and convergence of the equilibrium point of social power evolution are proved,and the characteristics of the corresponding equilibrium point of individual social power evolution are given.Finally,a simulation example is used to prove the correctness and rigor of the obtained theory.In Chapter 4,we study the problem of individual viewpoint evolution with forget-ful individuals in a cooperative competition network.The dynamic equation of individ-ual viewpoint evolution is represented by an individual viewpoint evolution model with forgetful individuals in a cooperative competition network.Firstly,different individual viewpoint evolution dynamic equations W₂₂are established using the lifting method for the influence weight matrix between forgetful individuals in structural non equilibrium and structural equilibrium states,respectively,Based on W₂₂these two different network state and structural equilibrium theories,the evolution characteristics of W₂₂individual viewpoints in corresponding states are obtained respectively.Finally,corresponding sim-ulation examples are given to verify the authenticity and correctness of the conclusions.Chapter 5 summarizes the full text,analyzes the issues that need to be optimized in this study,and looks forward to further work and future research directions.