Date Thesis Awarded

4-2019

Document Type

Honors Thesis

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Leah Shaw

Committee Members

Rex Kincaid

Drew LaMar

Abstract

We present a model for opinion dynamics on a network. Opinions are assumed to be a continuous variable, reflecting a possible spectrum of real world opinions. A node’s opinion is updated to become more similar to a randomly selected neighbor’s opinion, provided that the neighbor’s opinion differs by less than a threshold. Initially considering a static network, we establish criteria to determine whether consensus or clustering will be the outcome of the dynamics and on what time scales these states will be reached. We find that smaller step size of opinion update will facilitate consensus formation in the network. Next, in contrast to the static networks with fixed structures, we incorporate the changing nature of the interpersonal relations in real-life social networks. In addition to the opinion dynamics, links that do not communicate due to divergent opinions may be broken with some probability and new links are randomly created. In this way, the network changes in an adaptive manner, which combines the topological evolution of the network with dynamics in the network nodes. Our investigation reveals that adaptation fosters the formation of larger clusters at small mean degrees, while it promotes the division of the major cluster at comparatively large mean degrees.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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