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Title: Pattern selection and super-patterns in the bounded confidence model

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:
 [1] ;  [2]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Univ. of Minnesota, Minneapolis, MN (United States)
Publication Date:
OSTI Identifier:
1234245
Report Number(s):
LA-UR--15-24960
Journal ID: ISSN 0295-5075
Grant/Contract Number:
AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Europhysics Letters
Additional Journal Information:
Journal Volume: 112; Journal Issue: 1; Journal ID: ISSN 0295-5075
Publisher:
IOP Publishing
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING