论文标题
对超图的意见动力学模型的密度描述
A density description of a bounded-confidence model of opinion dynamics on hypergraphs
论文作者
论文摘要
社交互动通常同时发生三个或更多代理之间。检查有关超图的意见动力，使人们可以研究这种多元相互作用对代理观点的影响。在本文中，我们考虑了一个有限的信心模型（BCM），其中意见以连续的价值观和互动代理构成他们的意见，如果它们彼此足够亲密。我们研究了脱脂的密度描述 - 韦斯布赫BCM在超图上。随着代理的数量变得无限，我们得出了平均场意见密度的速率方程，我们证明该速率方程产生的概率密度将收敛到非互动意见集群。使用数值模拟，我们检查了基于密度的BCM稳态意见集群的分叉，并证明基于代理的BCM会收敛到BCM的密度描述，因为代理的数量变得无限。
Social interactions often occur between three or more agents simultaneously. Examining opinion dynamics on hypergraphs allows one to study the effect of such polyadic interactions on the opinions of agents. In this paper, we consider a bounded-confidence model (BCM), in which opinions take continuous values and interacting agents comprise their opinions if they are close enough to each other. We study a density description of a Deffuant--Weisbuch BCM on hypergraphs. We derive a rate equation for the mean-field opinion density as the number of agents becomes infinite, and we prove that this rate equation yields a probability density that converges to noninteracting opinion clusters. Using numerical simulations, we examine bifurcations of the density-based BCM's steady-state opinion clusters and demonstrate that the agent-based BCM converges to the density description of the BCM as the number of agents becomes infinite.
