论文标题
Axelrod模型的新型分析公式
A novel analytical formulation of the Axelrod model
论文作者
论文摘要
文化传播的Axelrod模型已在统计力学领域进行了广泛研究。该基于代理的模型的传统版本是为每个代理商分配$ f $组成部分的文化矢量，每个组件都可以采用$ q $文化特征之一。在这项工作中，我们介绍了一组新颖的平均场主方程，以描述$ f = 2 $和$ f = 3 $的模型，其中所有间接交互都是明确计算的。我们发现，不同宏观状态之间的过渡是由初始条件（由参数$ Q $设置的）和系统$ n $的大小驱动的，后者在主方程中衡量线性和立方术语之间的余额。我们还发现，这种分析方法完全与模拟完全吻合，在该模拟过程中，系统在动态过程中不会分解，并且与丢失链接有关的缩放关系会在发生这种情况时重新建立协议。
The Axelrod model of cultural dissemination has been widely studied in the field of statistical mechanics. The traditional version of this agent-based model is to assign a cultural vector of $F$ components to each agent, where each component can take one of $Q$ cultural trait. In this work, we introduce a novel set of mean field master equations to describe the model for $F=2$ and $F=3$ in complete graphs where all indirect interactions are explicitly calculated. We find that the transition between different macroscopic states is driven by initial conditions (set by parameter $Q$) and the size of the system $N$, who measures the balance between linear and cubic terms in master equations. We also find that this analytical approach fully agrees with simulations where the system does not break up during the dynamics and a scaling relation related to missing links reestablishes the agreement when this happens.
