有界置信模型中的模式选择与超模式
Pattern Selection and Super-patterns in the Bounded Confidence Model
摘要：
研究了观点动力学的有界置信模型中的斑图形成问题。在这个随机过程中，意见被一个单一的变量量化。两个代理人可以相互作用并达成公平的妥协，但前提是他们的意见分歧低于一个固定的阈值。从具有紧支撑的意见的均匀分布开始，形成行波，并且它从域边界传播到不稳定的均匀状态。因此，该系统达到一个稳定状态，孤立的集群是由大于相互作用范围的距离分开。这些团簇形成准周期性图案，其中团簇的大小和它们之间的间隔几乎是恒定的。我们解析地得到了簇之间的平均间隔L。有趣的是，也有非常小的准周期调制的大小的集群。这些调制的空间周期是从无理平均间隔L的连分数表示得出的一系列整数。
英文摘要：
We study pattern formation in the bounded confidence model of opinion dynamics. In this random process, opinion is quantified by a single variable. Two agents may interact and reach a fair compromise, but only if their difference of opinion falls below a fixed threshold. Starting from a uniform distribution of opinions with compact support, a traveling wave forms and it propagates from the domain boundary into the unstable uniform state. Consequently, the system reaches a steady state with isolated clusters that are separated by distance larger than the interaction range. These clusters form a quasi-periodic pattern where the sizes of the clusters and the separations between them are nearly constant. We obtain analytically the average separation between clusters L. Interestingly, there are also very small quasi-periodic modulations in the size of the clusters. The spatial periods of these modulations are a series of integers that follow from the continued fraction representation of the irrational average separation L.
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