Finite-size effects on the convergence time in continuous-opinion dynamics,Physical Review E

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Finite-size effects on the convergence time in continuous-opinion dynamics
Physical Review E ( IF 2.2 ) Pub Date : 2021-07-19 , DOI: 10.1103/physreve.104.014309
Hang-Hyun Jo ₁ , Naoki Masuda _{2,

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Affiliation

We study finite-size effects on the convergence time in a continuous-opinion dynamics model. In the model, each individual's opinion is represented by a real number on a finite interval, e.g., [0,1], and a uniformly randomly chosen individual updates its opinion by partially mimicking the opinion of a uniformly randomly chosen neighbor. We numerically find that the characteristic time to the convergence increases as the system size increases according to a particular functional form in the case of lattice networks. In contrast, unless the individuals perfectly copy the opinion of their neighbors in each opinion updating, the convergence time is approximately independent of the system size in the case of regular random graphs, uncorrelated scale-free networks, and complete graphs. We also provide a mean-field analysis of the model to understand the case of the complete graph.

中文翻译：

连续意见动力学中收敛时间的有限尺寸效应

我们研究了连续意见动力学模型中收敛时间的有限大小效应。在该模型中，每个人的意见由有限区间上的实数表示，例如，[0,1]，并且均匀随机选择的个体通过部分模仿均匀随机选择的邻居的意见来更新其意见。我们从数值上发现，在格网络的情况下，根据特定功能形式，随着系统规模的增加，收敛的特征时间会增加。相比之下，除非个体在每次意见更新中完美地复制邻居的意见，否则在规则随机图、不相关的无标度网络和完整图的情况下，收敛时间近似独立于系统大小。

更新日期：2021-07-19

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