Analysis and modelling of opinion dynamics in social networks

With the ever-growing speed of technology, individuals in a social network can influence each other's opinions on various issues, such as health, finance, or politics. Hence, it is of utmost importance to comprehend the underlying structure of opinion dynamics in social networks. Understanding how opinions are formed in a social network and the patterns of relationships among individuals can help us realize the weaknesses, strengths, and interests of individuals. Due to its importance, in this thesis, we aim to study the changing nature of opinions in social networks. In addition, we know from social psychology that designing experiments that include human trials can be very challenging. Therefore, we plan to utilize mathematical and social psychological theories to propose novel mathematical models which capture the dynamics of opinions in social networks. In Chapter 3, we model how people sort the opinions they receive from the social network. In our proposed model, individuals choose to accept, reject, or not commit to other individuals' opinions. We provide a rigorous analysis of the model and show that although rejection of opinions can cause an unbalance in the social network, eventually the model seeks to balance the network. In Chapter 4, we consider a social network in which there exist information sources and followers. We show that it is necessary for the sources to gain the trust of the followers to be able to contain their opinions. That is, the opinions of the individuals in the social network remain within the opinion range of the sources. In Chapter 5, we study how individuals' self-esteem evolves under the effect of opinions in their social network. In fact, we hypothesize that a change in a person's opinion in a discussion is a result of influences they received from the social network. We then study the effect of this influence on the evolution of the self-esteem of individuals in the same social network. In Chapter 6, we study how individuals' actions and opinions can affect others in a social network. To this end, in our proposed model, the individuals are free to choose an action from a binary set while holding an opinion towards that action. We provide rigorous convergence analysis and demonstrate how our model can be applied to real-world phenomena such as polarization and pluralistic ignorance.