Ergodicity properties of opinion models

Abstract

In this thesis, we study the long time behaviour of two specific models; the Compass model and the Deffuant model, which are special examples of opinion models. Opinion models are special stochastic Markov processes in which one wants to understand how global opinions can be formed given specific types of interaction. Both models are first introduced as Markov processes and then simulated numerically and compared. The numerical simulations verify known analytical results on their respective ergodic properties. Furthermore, the impact of two different types of noise, the uniform and the bi-modal noise, on both models is analysed using numerical simulations. The goal is to gain insight into the influence of the noise on the behaviour of the models. From the simulations we conclude that small uniform noise has little influence on the model behaviour. In contrast, even the smallest bi-modal noise changes the ergodic properties of the Compass model significantly, while not impacting the Deffuant model much.