Pattern selection and super-patterns in the bounded confidence model
Abstract
We study pattern formation in the bounded confidence model of opinion dynamics. In this random process, opinion is quantified by a single variable. Two agents may interact and reach a fair compromise, but only if their difference of opinion falls below a fixed threshold. Starting from a uniform distribution of opinions with compact support, a traveling wave forms and it propagates from the domain boundary into the unstable uniform state. Consequently, the system reaches a steady state with isolated clusters that are separated by distance larger than the interaction range. These clusters form a quasi-periodic pattern where the sizes of the clusters and the separations between them are nearly constant. We obtain analytically the average separation between clusters L. Interestingly, there are also very small quasi-periodic modulations in the size of the clusters. Furthermore, the spatial periods of these modulations are a series of integers that follow from the continued-fraction representation of the irrational average separation L.
- Authors:
-
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. of Minnesota, Minneapolis, MN (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1234245
- Report Number(s):
- LA-UR-15-24960
Journal ID: ISSN 0295-5075
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Europhysics Letters
- Additional Journal Information:
- Journal Volume: 112; Journal Issue: 1; Journal ID: ISSN 0295-5075
- Publisher:
- IOP Publishing
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Mathematics
Citation Formats
Ben-Naim, E., and Scheel, A. Pattern selection and super-patterns in the bounded confidence model. United States: N. p., 2015.
Web. doi:10.1209/0295-5075/112/18002.
Ben-Naim, E., & Scheel, A. Pattern selection and super-patterns in the bounded confidence model. United States. https://doi.org/10.1209/0295-5075/112/18002
Ben-Naim, E., and Scheel, A. Mon .
"Pattern selection and super-patterns in the bounded confidence model". United States. https://doi.org/10.1209/0295-5075/112/18002. https://www.osti.gov/servlets/purl/1234245.
@article{osti_1234245,
title = {Pattern selection and super-patterns in the bounded confidence model},
author = {Ben-Naim, E. and Scheel, A.},
abstractNote = {We study pattern formation in the bounded confidence model of opinion dynamics. In this random process, opinion is quantified by a single variable. Two agents may interact and reach a fair compromise, but only if their difference of opinion falls below a fixed threshold. Starting from a uniform distribution of opinions with compact support, a traveling wave forms and it propagates from the domain boundary into the unstable uniform state. Consequently, the system reaches a steady state with isolated clusters that are separated by distance larger than the interaction range. These clusters form a quasi-periodic pattern where the sizes of the clusters and the separations between them are nearly constant. We obtain analytically the average separation between clusters L. Interestingly, there are also very small quasi-periodic modulations in the size of the clusters. Furthermore, the spatial periods of these modulations are a series of integers that follow from the continued-fraction representation of the irrational average separation L.},
doi = {10.1209/0295-5075/112/18002},
journal = {Europhysics Letters},
number = 1,
volume = 112,
place = {United States},
year = {Mon Oct 26 00:00:00 EDT 2015},
month = {Mon Oct 26 00:00:00 EDT 2015}
}
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