A Density Description of a Bounded-Confidence Model of Opinion Dynamics on Hypergraphs

IF 1.9 4区 数学 Q1 MATHEMATICS, APPLIED
Weiqi Chu, Mason A. Porter
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引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2310-2328, December 2023.
Abstract. Social interactions often occur between three or more agents simultaneously. Examining opinion dynamics on hypergraphs allows one to study the effect of such polyadic interactions on the opinions of agents. In this paper, we consider a bounded-confidence model (BCM), in which opinions take continuous values and interacting agents comprise their opinions if they are close enough to each other. We study a density description of a Deffuant–Weisbuch BCM on hypergraphs. We derive a rate equation for the mean-field opinion density as the number of agents becomes infinite, and we prove that this rate equation yields a probability density that converges to noninteracting opinion clusters. Using numerical simulations, we examine bifurcations of the density-based BCM’s steady-state opinion clusters and demonstrate that the agent-based BCM converges to the density description of the BCM as the number of agents becomes infinite.
超图上意见动态有界置信度模型的密度描述
SIAM应用数学学报,83卷,第6期,2310-2328页,2023年12月。摘要。社会互动通常同时发生在三个或更多的主体之间。研究超图上的意见动态可以让人们研究这种多元互动对代理人意见的影响。在本文中,我们考虑了一个有界置信模型(BCM),在该模型中,意见取连续值,如果相互作用的智能体彼此足够接近,则构成它们的意见。研究了超图上Deffuant-Weisbuch BCM的密度描述。当智能体的数量变得无限时,我们推导了平均场意见密度的速率方程,并证明了该速率方程产生了收敛到非相互作用意见聚类的概率密度。通过数值模拟,我们研究了基于密度的BCM稳态意见聚类的分叉,并证明了当智能体的数量变得无限时,基于智能体的BCM收敛于BCM的密度描述。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
3.60
自引率
0.00%
发文量
79
审稿时长
12 months
期刊介绍: SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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