非标准规范下有界置信度下的投票动力学模型

IF 1.2 4区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Networks and Heterogeneous Media Pub Date : 2022-01-01 DOI:10.3934/nhm.2022032

S. Pilyugin, M. Tarasova, Aleksandr S. Tarasov, G. Monakov

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引用次数: 0

摘要

本文研究了基于Hegselmann和Krause提出的“有界置信”原理的意见动态模型。根据这一原则，选民参与有两个选择的选举决策时，会受到与自己观点相似的个人的影响。我们考虑了对该模型的一种修改，其中将生成描述社会意见最终分布形成过程的动力系统的算子定义为两个步骤。首先，对代理人的意见加上与其“影响组”中的意见成比例的值，然后将结果数组中的元素除以元素的最大绝对值，使意见保持在规定的区间内。我们证明了在适当的条件下，任何轨迹都趋向于一个不动点，并且所有剩余的不动点都是李雅普诺夫稳定的。

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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A model of voting dynamics under bounded confidence with nonstandard norming

In this paper, we study a model of opinion dynamics based on the so-called "bounded confidence" principle introduced by Hegselmann and Krause. Following this principle, voters participating in an electoral decision with two options are influenced by individuals sharing an opinion similar to their own.We consider a modification of this model where the operator generating the dynamical system which describes the process of formation the final distribution of opinions in the society is defined in two steps. First, to the opinion of an agent, a value proportional to opinions in his/her "influence group" is added, and then the elements of the resulting array are divided by the maximal absolute value of elements to keep the opinions in the prescribed interval. We show that under appropriate conditions, any trajectory tends to a fixed point, and all the remaining fixed points are Lyapunov stable.

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来源期刊

Networks and Heterogeneous Media 数学-数学跨学科应用

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： NHM offers a strong combination of three features: Interdisciplinary character, specific focus, and deep mathematical content. Also, the journal aims to create a link between the discrete and the continuous communities, which distinguishes it from other journals with strong PDE orientation. NHM publishes original contributions of high quality in networks, heterogeneous media and related fields. NHM is thus devoted to research work on complex media arising in mathematical, physical, engineering, socio-economical and bio-medical problems.