Inhomogeneous Hegselmann–Krause models with two types of noise

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2024-10-01 DOI:10.1016/j.automatica.2024.111948

Linglong Du , Yue Wang , Ke Wang

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引用次数: 0

Abstract

We derive two types of stochastic Hegselmann–Krause opinion formation models with leadership, study their different asymptotic behaviors and the noise effect to the leader’s control. Firstly, we propose a stochastic model with a multiplicative noise, which mimics the randomness from communication uncertainty. Using the Lyapunov functional approach, we provide a sufficient condition leading to the almost surely consensus behavior, which partially explains the mechanism that the group with large size and strong leadership can tolerate strong noise produced by communication uncertainty. The second noise comes from environmental uncertainty, fluctuates the system and makes opinions diverse and inclusive. We derive a stochastic model with additive noise, show that the noise from the environment destroys the leadership. However, the relative fluctuations of the followers’ opinions around the leader’s opinion have a uniformly bounded variance, which means they are still in a same group with the leader’s control. Finally, numerical simulations are performed to confirm theoretical results and explore more findings.

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具有两种噪声的非均质海格塞曼-克劳斯模型

我们推导了两类具有领导力的随机 Hegselmann-Krause 意见形成模型，研究了它们的不同渐近行为以及噪声对领导者控制力的影响。首先，我们提出了一种带有乘法噪声的随机模型，它模拟了交流不确定性带来的随机性。利用李亚普诺夫函数方法，我们提供了一个充分条件，导致几乎肯定的共识行为，这部分解释了规模大、领导力强的群体可以容忍通信不确定性产生的强噪声的机制。第二种噪音来自于环境的不确定性，它使系统产生波动，并使意见具有多样性和包容性。我们推导了一个具有加性噪声的随机模型，表明来自环境的噪声会破坏领导力。然而，追随者的意见围绕领导者意见的相对波动具有均匀有界的方差，这意味着他们在领导者的控制下仍处于同一群体中。最后，我们进行了数值模拟，以证实理论结果并探索更多发现。

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

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.