双层网络上不同时间演化尺度的耦合传播动力学

doi:10.3969/j.issn.1000-5641.2022.02.006

华东师范大学学报（自然科学版） ›› 2022, Vol. 2022 ›› Issue (2): 45-54.doi: 10.3969/j.issn.1000-5641.2022.02.006

双层网络上不同时间演化尺度的耦合传播动力学

曾颖琪¹, 唐明^1,^2,*()

1. 华东师范大学通信与电子工程学院, 上海　200241
2. 华东师范大学物理与电子科学学院, 上海　200241

收稿日期:2020-11-11 出版日期:2022-03-25 发布日期:2022-03-28
通讯作者: 唐明 E-mail:mtang@ce.ecnu.edu.cn
基金资助:
国家自然科学基金(11975099)

Coupled propagation dynamics of different time evolution scales on double-layer networks

Yingqi ZENG¹, Min TANG^1,^2,*()

1. School of Communication and Electronic Engineering, East China Normal University, Shanghai　200241, China
2. School of Physics and Electronic Science, East China Normal University, Shanghai　200241, China

Received:2020-11-11 Online:2022-03-25 Published:2022-03-28
Contact: Min TANG E-mail:mtang@ce.ecnu.edu.cn

摘要/Abstract

摘要：

基于双层网络构建了一个具有不同时间演化尺度的耦合传播模型—噪声投票-SIR (Susceptible-Infected-Recovery)传播耦合模型. 该模型可以用微观马尔可夫链数值分析方法来描述. 大量的蒙特卡洛模拟实验验证了这一数值分析方法的准确性. 研究发现, 耦合模型中发生了相变类型的跨越现象: 当意见形成过程中的噪声比较小的时候, 消息传播规模和正 $ \left( + \right) $ 意见比例随着传播速率的变化发生不连续相变, 与此同时还出现了磁滞回线和双稳态现象, 并能观察到全局意见共识的形成; 当噪声较大时, 两个动力学过程的序参量随传播速率的改变发生连续相变.

关键词: 双层网络, 时间演化尺度, 耦合传播, 相变, 跨越现象

Abstract:

Using double-layer networks, we constructed a coupled propagation model (Noisy Voter - Susceptible-Infected-Recovery) with different time evolution scales. This coupled spreading process can be characterized by numerical analysis method of microscopic Markov chain theory. We verified the accuracy of the proposed numerical analysis method using a large number of Monte Carlo simulation experiments. We found a crossover phenomenon of the phase transition type in the coupled model. Specifically, when the noise in the opinion formation process is relatively small, the information propagation scale and the proportion of positive opinions change discontinuously with the information transmission rate. At the same time, the hysteresis loop and bistability phenomenon appear, in which the phenomenon of global consensus can be observed. When the noise is large, the order parameters of these two dynamic processes vary continuously with the transmission rate.

Key words: double-layer networks, time evolution scales, coupled propagation, phase transition, crossover phenomenon

中图分类号:

TP393

曾颖琪, 唐明. 双层网络上不同时间演化尺度的耦合传播动力学[J]. 华东师范大学学报（自然科学版）, 2022, 2022(2): 45-54.

Yingqi ZENG, Min TANG. Coupled propagation dynamics of different time evolution scales on double-layer networks[J]. Journal of East China Normal University(Natural Science), 2022, 2022(2): 45-54.

图/表 5

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层间影响	联合状态
层间影响	$ \left[ + \mathrm{S}\right] $	$ \left[ + \mathrm{R}\right] $	$ \left[-\mathrm{S}\right] $	$ \left[-\mathrm{R}\right] $
A层对B层的影响	$ {\psi }_{i}\left(t\right)=1 + \epsilon $	$ {\psi }_{i}\left(t\right)=1 + \epsilon $	$ {\psi }_{i}\left(t\right)=1-\epsilon $	$ {\psi }_{i}\left(t\right)=1-\epsilon $
B层对A层的影响	$ {\xi }_{i}^{-}\left(t\right)=1 + \epsilon $	$ {\xi }_{i}^{-}\left(t\right)=1-\epsilon $	$ {\xi }_{i}^{ + }\left(t\right)=1-\epsilon $	$ {\xi }_{i}^{ + }\left(t\right)=1 + \epsilon $

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双层网络上不同时间演化尺度的耦合传播动力学

Coupled propagation dynamics of different time evolution scales on double-layer networks

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