Consensus and clustering in opinion formation on networks

Bujalski, Julia; Dwyer, Grace; Kapitula, Todd; Le, Quang-Nhat; Malvai, Harjasleen; Rosenthal-Kay, Jordan; Ruiter, Joshua

doi:10.1098/rsta.2017.0186

Cited by 9 publications

(8 citation statements)

References 34 publications

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“…Each city is assumed to have internal opinion dynamics as described by the original system (1.1), and then there would be some coupling between the cities. This problem of interacting cities, each of which is composed only of congregators who follow the Marvel et al [7] model, was investigated in Bujalski et al [4]. One of the interesting findings in that paper is that increasing interaction strength between individual cities leads to a clustering phenomena.…”

Section: Resultsmentioning

confidence: 98%

“…After that, we will assume there are zealots for opinion 1. As seen in the case of all congregators (see [4] and the references therein), it is known that there is a threshold such that if the proportion of zealots is above that threshold value, then the entire population will hold the same opinion as the zealots. We examine how the presence of contrarians effects this result, and to determine the manner in which they effect the size of the interval (X − , X + ).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Opinion Formation Dynamics with Contrarians and Zealots

Eekhoff¹

2019

SIURO

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Mean-field type ODE models for opinion dynamics often assume that the entire population is comprised of congregators, who are agreeable. On the other hand, a contrarian opinion dynamics ODE model assumes the population has two personality types: congregators, and contrarians, who are disagreeable. In this paper we broadly study how contrarians influence the ability of the population to form a fixed and stable opinion. In particular, we re-examine the dynamics associated with the model introduced by Tanabe and Masuda [12] by looking at how the parameters effect the formation of stable periodic solutions (whose existence implies there is no fixed consensus opinion). Afterwards, we refine and analyze the model under two new hypotheses: (a) the contrarians bow to peer pressure and change their personality type to congregators if a large enough proportion of the entire population agrees on an opinion, and (b) there are zealots associated with one of the opinions. We conclude with a brief discussion on possible extensions of this work.

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Section: Resultsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Opinion Formation Dynamics with Contrarians and Zealots

Eekhoff¹

2019

SIURO

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“…The nonlinear coupling term for the model Equation (7) takes into account the average proportion of speakers of language 𝑈 and language 𝑉 for all other groups, and is clearly very different from the linear coupling term associated with the model Equation (6). It is an open question as to whether this functional difference in the coupling terms leads to a qualitative difference in the dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…The MS model was extended to networks in Ref. 7, and this extended model was studied using dynamical systems techniques. Tanabe and Masuda 31 proposed and analyzed an interesting opinion formation model (hereafter labelled TM) in which it was assumed that the population itself breaks down into two groups: congregators and contrarians.…”

Section: Introductionmentioning

confidence: 99%

Language competition on lattices

Kapitula

Kevrekidis

2021

Stud Appl Math

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We consider a language dynamics ODE model for two languages on a square lattice. The model is an extension of the one popularized by Abrams and Strogatz. In our study, we are interested in the existence and spectral stability of structures such as stripes, which are realized through pulses and/or the concatenation of fronts, and spots, which are a contiguous collection of sites in which one language is dominant. Because the coupling between adjacent sites is nonlinear, the transition between regions speaking two different languages is super‐exponential. The full dynamics are considered as a function of the prestige of a language. It is seen that as the prestige varies, it allows for a language to spread through the lattice, or conversely for its demise. Although most of the work is done assuming a square lattice, we briefly consider the problem on a triangle lattice to illustrate the robustness of the findings. We conclude by looking at the existence and spectral stability of fronts and pulses for an associated continuum PDE model. In this model, the super‐exponential decay associated with the lattice model is reflected in the existence of compactly supported structures (compactons).

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“…the proportions of the total population that are in one of the mentioned states are tracked down. Bujalski et al [48] herein propose an extension of the system from [47]. In particular, conditions under which consensus and pluralism occur and the influence of zealots in the dynamics of forming an opinion are understood.…”

mentioning

confidence: 99%

Stability of nonlinear waves and patterns and related topics

Ghazaryan

Lafortune

Manukian

2018

Phil. Trans. R. Soc. A.

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Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i.e. the nature of the instability, and also coherent structures that appear as a result of an instability of travelling waves. A variety of analytical, numerical and hybrid techniques are used to study travelling waves and their properties.This article is part of the theme issue 'Stability of nonlinear waves and patterns and related topics'.

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Consensus and clustering in opinion formation on networks

Cited by 9 publications

References 34 publications

Opinion Formation Dynamics with Contrarians and Zealots

Opinion Formation Dynamics with Contrarians and Zealots

Language competition on lattices

Stability of nonlinear waves and patterns and related topics

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