Research On The Opinion Dynamic Model With Competitive Behavior

With the development of urbanization and the rise of new communication technology,the way of human information communication has changed unprecedentedly.Various information exchange methods and platforms such as Facebook and Douyin have emerged one after another.The way people obtain information and participate in discussions has also undergone tremendous changes compared with the past.These factors not only increase the amount of information in the social network,but also make the interaction and decision-making among individuals more complex.In this case,it is even more significant to discuss the generation,diffusion and aggregation of group concepts.Competition and confrontation are often ubiquitous in social groups.Therefore,in this article,we mainly study the evolutionary laws of ideas under the competitive mechanism.At the same time,we also consider the influence of switching topology and stubbornness on the evolution of ideas.First,we propose the opinion dynamic model with competitive relations and switching topology,and analyze the convergence of the model using the knowledge of spectrum analysis and matrix theory,aiming at the network topology as structurally balanced and structurally unbalanced.The situation has been met with a number of conditions for the opinion to be consensus or bipartite consensus.And use numerical simulation to verify the validity of the obtained results.Secondly,we study the opinion dynamic model with competitive behavior and stubborn individuals.In this model,in addition to competition,we also consider the prejudice and stubbornness that may exist in social networks.The so-called stubbornness refers to the characteristics of individuals that are difficult to persuade and change.The existence of these stubborn individuals is often the main cause of grouping.Regarding the situation that the network topology is structurally balanced and structurally unbalanced,we give several conditions for network convergence.These conditions depend on the network topology and stubborn coefficients.The opinion of convergence often forms multiple clusters,that is,it is difficult for the opinion to achieve consensus in the model.At the same time,we use numerical simulation to verify our results.At the end of this article,we summarize and generalize the work we have done,and look forward to the future research direction of opinion dynamics.Our research and its results have certain practical significance for enriching the research connotation of opinion dynamics and revealing the development law of opinion generation,diffusion and aggregation.