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The Occurrences of Sliding Solutions in the Hegselmann-Krause Model

Bertamini, Leonardo (2023) The Occurrences of Sliding Solutions in the Hegselmann-Krause Model. Bachelor's Thesis, Mathematics.


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This project investigated the Hegselmann-Krause model in opinion dynamics. This paper followed a previous paper that investigated the stability of the model and its convergence. The occurrences of sliding solutions due to discontinuities in the model was investigated. This means that the vector field varies discontinuously as solutions approach a surface. At this point, solutions can display many different behaviours, but this paper focused on the case where the solution slides along the switching surface. To do this the model will be viewed as a discontinuous piecewise linear model. This paper is significant as it improved the understanding of an important model in the field of opinion dynamics. Each zone was investigated and extended to the different boundary cases. Patterns were investigated to make more general proofs. This project proved no sliding solutions in the super symmetric case. The asymmetric case proved to be complex but no sliding solutions could be constructed in three dimensions. However, no evidence was found that they could not exist in higher dimensions

Item Type: Thesis (Bachelor's Thesis)
Supervisor name: Trenn, S.
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 21 Feb 2023 14:06
Last Modified: 21 Feb 2023 14:13

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