Tsukuba University, Faculty of Engineering, Information and Systems, Tsukuba, Ibaraki, Japan.
University of Tokyo, Research Center for Advanced Science and Technology, Megro, Tokyo, Japan.
PLoS One. 2018 Apr 24;13(4):e0195988. doi: 10.1371/journal.pone.0195988. eCollection 2018.
Collective behaviors that seem highly ordered and result in collective alignment, such as schooling by fish and flocking by birds, arise from seamless shuffling (such as super-diffusion) and bustling inside groups (such as Lévy walks). However, such noisy behavior inside groups appears to preclude the collective behavior: intuitively, we expect that noisy behavior would lead to the group being destabilized and broken into small sub groups, and high alignment seems to preclude shuffling of neighbors. Although statistical modeling approaches with extrinsic noise, such as the maximum entropy approach, have provided some reasonable descriptions, they ignore the cognitive perspective of the individuals. In this paper, we try to explain how the group tendency, that is, high alignment, and highly noisy individual behavior can coexist in a single framework. The key aspect of our approach is multi-time-scale interaction emerging from the existence of an interaction radius that reflects short-term and long-term predictions. This multi-time-scale interaction is a natural extension of the attraction and alignment concept in many flocking models. When we apply this method in a two-dimensional model, various flocking behaviors, such as swarming, milling, and schooling, emerge. The approach also explains the appearance of super-diffusion, the Lévy walk in groups, and local equilibria. At the end of this paper, we discuss future developments, including extending our model to three dimensions.
群体行为表现出高度有序性，并呈现出集体一致性，例如鱼类的群体游动和鸟类的集群行为，这源于群体内部的无缝洗牌（如超级扩散）和喧闹（如 Lévy 游走）。然而，这种群体内部的嘈杂行为似乎排除了集体行为：直观地说，我们期望嘈杂的行为会导致群体不稳定，并分裂成小的子群体，而高度的一致性似乎排除了邻居的洗牌。尽管具有外部噪声的统计建模方法，如最大熵方法，提供了一些合理的描述，但它们忽略了个体的认知视角。在本文中，我们试图解释群体趋势（即高度一致性）和高度嘈杂的个体行为如何在单个框架中共存。我们方法的关键方面是多时间尺度相互作用，这种相互作用源于存在一个反映短期和长期预测的相互作用半径。这种多时间尺度相互作用是许多群体模型中吸引力和对齐概念的自然扩展。当我们将这种方法应用于二维模型时，各种群体行为，如聚集、盘旋和集体游动，都会出现。该方法还解释了超级扩散、群体中的 Lévy 游走和局部平衡的出现。在本文的最后，我们讨论了未来的发展，包括将我们的模型扩展到三维。
