Pattern selection and super-patterns in the bounded confidence model. (26th October 2015)

• Record Type: Journal Article
• Authors: Ben-Naim, E.; Scheel, A.
• Is Part Of: Europhysics letters. Volume 112:Number 1(2015:Oct.)
• Publication Date: 2015-10-26
• Subjects: 89.75.Kd -- 82.40.Ck -- 05.45.-a; Physics -- Periodicals; Electronic journals; 530.05
• DOI: 10.1209/0295-5075/112/18002
• Languages: English
• ISSNs: 0295-5075

Abstract

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. The spatial periods of these modulations are a series of integers that follow from the continued-fraction representation of the irrational average separation L .