具有随机异步规则的有界置信意见动力学的拟同步
Quasi-synchronization of bounded confidence opinion dynamics with stochastic asynchronous rule
摘要：
近年来，噪声诱导的Hegselmann-Krause（HK）动力学同步理论得到了很好的发展。作为一个典型的有界置信度的意见动态，HK模型服从同步更新规则，即，\emph{all}代理在每个时间点检查并更新其意见。然而，异步有界置信模型，包括著名的Deffuant-Weisbuch（DW）模型，是否可以被噪声同步尚未得到理论证明。本文提出了一个具有随机异步规则的广义有界置信模型。该模型以DW模型和HK模型为特例，将有界置信模型推广到实际应用中。我们发现，异步模型具有不同的基于噪声的同步行为相比，同步HK模型。一般来说，在噪声驱动下，HK动力学可以实现准同步\emph{almost surely}。对于非同步动力学，我们证明了该模型可以实现准同步\emph{in mean}，这是一种弱于“几乎必然”意义的新型准同步。该结果统一了有界置信度意见动力学的噪声诱导同步理论，并首次从理论上证明了DW模型的噪声诱导同步。此外，研究结果提供了一个理论基础，发展基于噪声的控制策略，更复杂的社会意见系统的随机异步规则。
英文摘要：
Recently the theory of noise-induced synchronization of Hegselmann-Krause (HK) dynamics has been well developed. As a typical opinion dynamics of bounded confidence, the HK model obeys a synchronous updating rule, i.e., \emph{all} agents check and update their opinions at each time point. However, whether asynchronous bounded confidence models, including the famous Deffuant-Weisbuch (DW) model, can be synchronized by noise have not been theoretically proved. In this paper, we propose a generalized bounded confidence model which possesses a stochastic asynchronous rule. The model takes the DW model and the HK model as special cases and can significantly generalize the bounded confidence models to practical application. We discover that the asynchronous model possesses a different noise-based synchronization behavior compared to the synchronous HK model. Generally, the HK dynamics can achieve quasi-synchronization \emph{almost surely} under the drive of noise. For the asynchronous dynamics, we prove that the model can achieve quasi-synchronization \emph{in mean}, which is a new type of quasi-synchronization weaker than the "almost surely" sense. The results unify the theory of noise-induced synchronization of bounded confidence opinion dynamics and hence proves the noise-induced synchronization of DW model theoretically for the first time. Moreover, the results provide a theoretical foundation for developing noise-based control strategy of more complex social opinion systems with stochastic asynchronous rules.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
