论文标题
连续开放动力学模型中共识的方法：一项受颗粒气体物理学启发的研究
Approach to consensus in models of continuous-opinion dynamics: a study inspired by the physics of granular gases
论文作者
论文摘要
通过利用其与单维颗粒气体的相似性，提出和研究了连续开放动力学的模型。代理在脱弗兰模型中的相互作用，与控制个人有说服力的参数$α$相互作用。相互作用与确定意见和速度的两种谷物在一条线上移动的碰撞规则相吻合，而$α$是所谓的正常恢复系数。从所有意见的概率密度的主方程开始，为系统达成共识提供了一般条件。相互作用频率与相对意见的$β$ - 功率成正比的情况更详细地研究。结果表明，对主方程的平均场近似值导致了舆论分布的玻尔兹曼动力学方程。在这种情况下，系统始终达成共识，可以看作是意见温度的零的方法，这是对意见分布的宽度的度量。此外，系统的长时间行为的特征是对玻尔兹曼方程的缩放解决方案，在该方程中，所有时间依赖性通过温度都会发生。 $β= 0 $的情况与脱芬模型有关，并且在分析上可溶。缩放分布是单峰的，独立于$α$。对于$β> 0 $，意见的分布低于$ |α| $的临界值，在其上方是多模式。这意味着代理在两极分化的同时可能达成共识。在临界点附近，对于$ |α| \ ge 0.4 $，意见分布符合两个高斯分布的总和。蒙特卡洛模拟与理论结果一致。
A model for continuous-opinion dynamics is proposed and studied by taking advantage of its similarities with a mono-dimensional granular gas. Agents interact as in the Deffuant model, with a parameter $α$ controlling the persuasibility of the individuals. The interaction coincides with the collision rule of two grains moving on a line, provided opinions and velocities are identified, with $α$ being the so-called coefficient of normal restitution. Starting from the master equation of the probability density of all opinions, general conditions are given for the system to reach consensus. The case when the interaction frequency is proportional to the $β$-power of the relative opinions is studied in more detail. It is shown that the mean-field approximation to the master equation leads to the Boltzmann kinetic equation for the opinion distribution. In this case, the system always approaches consensus, which can be seen as the approach to zero of the opinion temperature, a measure of the width of the opinion distribution. Moreover, the long-time behaviour of the system is characterized by a scaling solution to the Boltzmann equation in which all time dependence occurs through the temperature. The case $β=0$ is related to the Deffuant model and is analytically soluble. The scaling distribution is unimodal and independent of $α$. For $β>0$ the distribution of opinions is unimodal below a critical value of $|α|$, being multimodal with two maxima above it. This means that agents may approach consensus while being polarized. Near the critical points and for $|α|\ge 0.4$, the distribution of opinions is well approximated by the sum of two Gaussian distributions. Monte Carlo simulations are in agreement with the theoretical results.
