Physics (Internal)

Opinion Models on Complex Networks

This event is part of the PhD Final Oral Exams.

Dissertation Committee: H.E. Stanley, William Klein, Robert Carey, William Skocpol, Plamen Ivanov

ABSTRACT We focus on non-consensus opinion models in which above a certain threshold two opinions coexist in a stable relationship. We revisit and extend the non-consensus opinion (NCO) model introduced by Shao et al. The NCO model in random networks displays a second order phase transition that belongs to regular mean field percolation and is characterized by the appearance (above a certain threshold) of a large spanning cluster of the minority opinion. We generalize the NCO model by adding a weight factor W to each individual’s original opinion when determining their future opinion (NCOW model). We find that as W increases the minority opinion holders tend to form stable clusters with a smaller initial minority fraction than in the NCO model. We also study another non-consensus opinion model based on the NCO model, the inflexible contrarian opinion (ICO) model, which introduces inflexible contrarians to model the competition between two opinions in a steady state. Inflexible contrarians are individuals that never change their original opinion but may influence the opinions of others. The inflexible contrarians effectively decrease the size of the largest rival-opinion cluster. All of the above models have previously been explored in terms of a single network, but human communities are usually interconnected, not isolated. We study here the opinion dynamics in coupled networks. We find that the interdependent links effectively force the system from a second order phase transition, which is characteristic of the NCO model on a single network, to a hybrid phase transition, i.e., a mix of second-order and abrupt jump-like transitions that ultimately becomes, as we increase the percentage of v interdependent agents, a pure abrupt transition. We conclude that for the NCO model on coupled networks, interactions through interdependent links could push the non-consensus opinion model to a consensus opinion model, which mimics the reality that increased mass communication causes people to hold opinions that are increasingly similar. Moreover we also study the NCO model on directed networks. We define directionality as the percentage of unidirectional links in a network, and we use the linear correlation coefficient between the indegree and outdegree of a node to quantify the asymmetry between the indegree and outdegree. We introduce two degree-preserving rewiring approaches which allow us to construct directed networks that can have a broad range of possible combinations of directionality and linear correlation coefficient to further study how directionality and linear correlation coefficient impact opinion competitions. We find that as the directionality or the indegree and outdegree correlation coefficient increase the majority opinion spread better becoming more dominant and it becomes harder for the minority opinion to survive.