Opinion Dynamics in The Hegselmann-Krause Model on The Circle: Analysis and Simulation

Over the last decades, the problem of synchronization has been solving by many researchers. Opinion formation is one of the critical issues in sociology. By opinion formation we mean the changing opinions in a group of people even if they have different opinions at the beginning. In this senior thesis we consider Hegselmann-Krause model on a segment and modify this model on the circle. The study and analysis of consensus algorithms are based on matrix and graph theory. We will establish that there may be several results: either a group of people always achieves a consensus or there is a clustering of opinions, that is, in each cluster people hold the same opinion.Examples that support theoretical assumptions are given. We also developed programs on Python and Mathematica Wolfram which help to find out how many different opinions we have as a result. These technical tools plot graphs to see the general trend of solution to specific problems. Key words - opinion dynamics, Hegselmann-Krause model, bounded confidence, consensus problem, matrix theory.