Phase diagram of a multiple forces model for animal group formation: marches versus circles determined by the relative strength of alignment and cohesion
Phase diagram of a multiple forces model for animal group formation: marches versus circles determined by the relative strength of alignment and cohesion
复制标题
动物群体形成的多力模型的相图：行军与圆圈由对齐和凝聚力的相对强度决定
DOI：
10.1007/s10144-016-0544-3
复制
发表时间：
2016
影响因子：
1.7
通讯作者：
Yoh Iwasa
中科院分区：
文献类型：
--
作者：
Yuki Kubo;Yoh Iwasa
许多种类的鱼、鸟和昆虫组成一起活动的个体群体，称为群体、群或群，具有独特的形状和速度。在这里，我们研究一个模型，它跟踪许多个体的运动，其中每个个体以恒定的速度移动，并在交互半径内改变其移动角度以响应其邻居。在短距离的分离(或排斥)之外，每个个体都会改变移动方向，以达到与其邻居相似的移动方向(排列)，并向他们移动(凝聚力)。在相互作用范围内的每一对个体之间，结盟和凝聚力同时发挥作用(多力模型)。这与其他许多动物群体形成的模型不同，在这些模型中，两种力中只有一种在起作用(单力模型)，不同的力在个体之间距离的不同区域运行。根据对齐和凝聚力的相对强弱，我们的模型生成两组不同的模式：行进和圆圈。我们展示了取决于排列和内聚的相对强度的组模式的相图。随着相对凝聚力的排列强度的增加，群体的形状逐渐按以下顺序变化：(1)圆圈，(2)圆圈和行军的混合，(3)短行进，(4)长行进，(5)宽大行进。我们推导了圆的空间大小公式，它解释了圆的半径不随个体的数量而变化，而是随着移动速度的增加而增加，随着移动方向对邻域的敏感性而减小。
Many species of fish, bird, and insect form groups of individuals that move together, called schools, flocks, or swarms, of characteristic shape and speed. Here we study a model that traces movements of many individuals, in which each individual moves at a constant speed, and changes its movement angle in response to its neighbors within a radius of interaction. Outside of a short range of separation (or repulsion), each individual changes moving direction to achieve a similar moving direction as its neighbors (alignment) and to move toward them (cohesion). Between each pair of individuals within an interaction range, both alignment and cohesion are at work simultaneously (multiple forces model). This is different from many other models for animal group formation in which only one of the two forces is at work (single force model), different forces operating in different zones of between‐individual distance. Depending on the relative strength of alignment and cohesion, our model produces groups of two distinct patterns: marches and circles. We showed the phase diagram of group patterns depending on the relative strength of alignment and cohesion. As the strength of alignment relative to cohesion increases, the shapes of groups change gradually in the following order: (1) circles, (2) mixture of circles and marches, (3) short marches, (4) long marches, (5) wide marches. We derived a formula for the spatial size of circles, which explains that the radius of circles does not change with the number of individuals, but it increases with moving speed and decreases with the sensitivity of moving direction to neighbors.