Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton, FL, USA.
Department of Physics, Florida Atlantic University, Boca Raton, FL, USA.
J R Soc Interface. 2019 Aug 30;16(157):20190360. doi: 10.1098/rsif.2019.0360. Epub 2019 Aug 14.
Coordination in living systems-from cells to people-must be understood at multiple levels of description. Analyses and modelling of empirically observed patterns of biological coordination often focus either on ensemble-level statistics in large-scale systems with many components, or on detailed dynamics in small-scale systems with few components. The two approaches have proceeded largely independent of each other. To bridge this gap between levels and scales, we have recently conducted a human experiment of mid-scale social coordination specifically designed to reveal coordination at multiple levels (ensemble, subgroups and dyads) simultaneously. Based on this experiment, the present work shows that, surprisingly, a single system of equations captures key observations at all relevant levels. It also connects empirically validated models of large- and small-scale biological coordination-the Kuramoto and extended Haken-Kelso-Bunz (HKB) models-and the hallmark phenomena that each is known to capture. For example, it exhibits both multistability and metastability observed in small-scale empirical research (via the second-order coupling and symmetry breaking in extended HKB) and the growth of biological complexity as a function of scale (via the scalability of the Kuramoto model). Only by incorporating both of these features simultaneously can we reproduce the essential coordination behaviour observed in our experiment.
生命系统中的协调——从细胞到人类——必须在多个描述层次上理解。对生物协调的经验观察模式的分析和建模通常要么集中在具有许多组件的大规模系统的整体水平统计数据上，要么集中在具有少数组件的小规模系统的详细动力学上。这两种方法在很大程度上是相互独立的。为了弥合这一层次和规模之间的差距，我们最近进行了一项针对中规模社会协调的人类实验，该实验专门设计用于同时揭示多个层次（整体、子组和对偶）的协调。基于这项实验，本工作表明，令人惊讶的是，一个单一的方程组可以捕捉到所有相关层次的关键观察结果。它还将大型和小型生物协调的经验验证模型——Kuramoto 和扩展的 Haken-Kelso-Bunz（HKB）模型——以及每个模型已知捕获的标志性现象联系起来。例如，它表现出了小规模经验研究中观察到的多稳定性和亚稳定性（通过扩展 HKB 中的二阶耦合和对称破缺），以及生物复杂性作为尺度函数的增长（通过 Kuramoto 模型的可扩展性）。只有同时包含这两个特征，我们才能再现我们实验中观察到的基本协调行为。
