Noisy bounded confidence models for opinion dynamics: the effect of boundary conditions on phase transitions

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

IMA Journal of Applied Mathematics Pub Date : 2021-10-01 DOI:10.1093/imamat/hxab044

B D Goddard;B Gooding;H Short;G A Pavliotis

引用次数: 0

Abstract

We study SDE and PDE models for opinion dynamics under bounded confidence, for a range of different boundary conditions, with and without the inclusion of a radical population. We perform exhaustive numerical studies with pseudo-spectral methods to determine the effects of the boundary conditions, suggesting that the no-flux case most faithfully reproduces the underlying mechanisms in the associated deterministic models of Hegselmann and Krause. We also compare the SDE and PDE models, and use tools from analysis to study phase transitions, including a systematic description of an appropriate order parameter.

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意见动力学的噪声有界置信模型：边界条件对相变的影响

我们研究了在有界置信度下，在一系列不同的边界条件下，包括和不包括激进群体的意见动力学的SDE和PDE模型。我们用伪谱方法进行了详尽的数值研究，以确定边界条件的影响，这表明无通量情况最忠实地再现了Hegselmann和Krause的相关确定性模型中的潜在机制。我们还比较了SDE和PDE模型，并使用分析工具来研究相变，包括对适当顺序参数的系统描述。

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

IMA Journal of Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

8.30%

发文量

审稿时长

24 months

期刊介绍： The IMA Journal of Applied Mathematics is a direct successor of the Journal of the Institute of Mathematics and its Applications which was started in 1965. It is an interdisciplinary journal that publishes research on mathematics arising in the physical sciences and engineering as well as suitable articles in the life sciences, social sciences, and finance. Submissions should address interesting and challenging mathematical problems arising in applications. A good balance between the development of the application(s) and the analysis is expected. Papers that either use established methods to address solved problems or that present analysis in the absence of applications will not be considered. The journal welcomes submissions in many research areas. Examples are: continuum mechanics materials science and elasticity, including boundary layer theory, combustion, complex flows and soft matter, electrohydrodynamics and magnetohydrodynamics, geophysical flows, granular flows, interfacial and free surface flows, vortex dynamics; elasticity theory; linear and nonlinear wave propagation, nonlinear optics and photonics; inverse problems; applied dynamical systems and nonlinear systems; mathematical physics; stochastic differential equations and stochastic dynamics; network science; industrial applications.