Control of opinion dynamics in multiple dimensions

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The context of the researchThe fundamental concept of opinion dynamics, that a collection of individuals interacts and updates their opinions over time, has been represented in an ever-growing varity of models. In a simple model individuals update their opinions in discrete time steps by taking a weighted average of the opinions of those around them, leadinf to a linear dynamical system. For such systems there exists clear condistions for when consensus can arise and methods to predict what opinion the group will reach. This simple model has been develpoed in a range of different directions, some include more realistic features such as online media or stubborn individuals , propose different conditions for interaction, apply alternative mathematical techniques, or make any number of other adaptations.A major contribution is the models of Hegselmann and Krause, and Deffuant et al. which independently introduced bounded confidence: the idea that individuals only interact if thier opinions are already sufficeintly close. This condition creates nonlinearity and can lead to the formation of opinion clusters. This originally discrete time models has been adapted into continuous time models, then into stochastic models and finally into corrsponding PDE models describing the evolution of the opinion distribution in a large population. Under various parameter regimes these models can exhibit a range of interesting behaviours: in some scenarios opinions coalesce or become more moderate over time, in other cases multiple distinct opinions persist and in some cases no clear opinions emerge at all. With unprecendented access to the opinions of people across the world it is easy to see compareable situations in real life, with data from social media allowing the possibility of narrowing the gap between meathematical models and newly observable dynamics. The undeinable impact of online communication makes it increasingly important to develop our understnading of how individuals and groups opinions are formed and what can be done to avoid the spread of potentially dangerous disinformation.Due to the complex nature of opinion dynamics, especially in modes with individulaised agents, undelaying social networks or nonlinear interactions, it is often necessary to explore the behaviour of the model through extensive simulation.This project aims to improve the accuracy of opinion dynamics models by combining multidomensional opinions and dynamic network structure with existing models, and investigate the possibility of control in such systems.The objectives are to exten opinion dynamics models into multiple dimensions exploring different ways in which nodes may interact based on their opinions on various topics. Incorporate dynamic network structure to mirror how individuals relationships may evolve over time in response to their (dis)agreement on various topics. Use network structure and sentiment analaysis from Twitter data to observe real multidimensional opinion formation and compare this to the behaviuors observed in models.The novelty of the research methodologyWeighting the opinions of others natrually creates a network structure, and so the influence of social networks on opinion dynamics has been explored. However the conclusion of a dynamic network, in particular one in which the network structure is coupled with individuals opinions, is a novel development.The potential impact, applications and benefitsIf it is found that incorporating multiple opinions provides a more realistic model of opinion formation, an understanding of how such systems can be controlled could be useful in designing promotional campaigns, reducing the impace of misinformation or encoraging/ discouraging cooperation between different organisations.This project falls into the mathematical sciences research area.External Partener - Improbable - will provide expertise in developing data driven models, will provide technical support.