Noisy bounded confidence models for opinion dynamics: the effect of boundary conditions on phase transitions
Abstract We study SDE and PDE models for opinion dynamics under bounded confidence, for a range of different boundary conditions, with and without the inclusion of a radical population. We perform exhaustive numerical studies with pseudo-spectral methods to determine the effects of the boundary cond...
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| Published in | IMA journal of applied mathematics Vol. 87; no. 1; pp. 80 - 110 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Oxford University Press
22.01.2022
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| Abstract | Abstract
We study SDE and PDE models for opinion dynamics under bounded confidence, for a range of different boundary conditions, with and without the inclusion of a radical population. We perform exhaustive numerical studies with pseudo-spectral methods to determine the effects of the boundary conditions, suggesting that the no-flux case most faithfully reproduces the underlying mechanisms in the associated deterministic models of Hegselmann and Krause. We also compare the SDE and PDE models, and use tools from analysis to study phase transitions, including a systematic description of an appropriate order parameter. |
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| AbstractList | We study SDE and PDE models for opinion dynamics under bounded confidence, for a range of different boundary conditions, with and without the inclusion of a radical population. We perform exhaustive numerical studies with pseudo-spectral methods to determine the effects of the boundary conditions, suggesting that the no-flux case most faithfully reproduces the underlying mechanisms in the associated deterministic models of Hegselmann and Krause. We also compare the SDE and PDE models, and use tools from analysis to study phase transitions, including a systematic description of an appropriate order parameter. Abstract We study SDE and PDE models for opinion dynamics under bounded confidence, for a range of different boundary conditions, with and without the inclusion of a radical population. We perform exhaustive numerical studies with pseudo-spectral methods to determine the effects of the boundary conditions, suggesting that the no-flux case most faithfully reproduces the underlying mechanisms in the associated deterministic models of Hegselmann and Krause. We also compare the SDE and PDE models, and use tools from analysis to study phase transitions, including a systematic description of an appropriate order parameter. |
| Author | Goddard, B D Pavliotis, G A Short, H Gooding, B |
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| Keywords | 82C26 bounded confidence 65M70 opinion dynamics phase transitions no-flux boundary conditions 2000 Math Subject Classification: 82C22 |
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We study SDE and PDE models for opinion dynamics under bounded confidence, for a range of different boundary conditions, with and without the... We study SDE and PDE models for opinion dynamics under bounded confidence, for a range of different boundary conditions, with and without the inclusion of a... |
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| Title | Noisy bounded confidence models for opinion dynamics: the effect of boundary conditions on phase transitions |
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