In animal groups, individual interactions achieve coordinated movements to maintain cohesion. In horse-harem groups, herding is a behaviour in which stallions chase mares from behind; it is considered to assist with group cohesiveness. The mechanisms of the group cohesion were studied using the methods of drone filming and video tracking during herding and two phases of interactions were found based on the mares’ timing of movement initiation. The study shows that mares that move first are those nearest to the stallion; while the movement initiation of the later mares is determined by the distance from the nearest moving mare. Thus, as a second step to the full understanding of group cohesion, we propose a mathematical model of mares herded by a harem stallion, which is a modification of a sheep model during shepherding. Our model is a linear combination of the five components: inertia, repulsion from the stallion, short-range repulsion, synchronisation attraction, and attraction to the centre of the group. We tune the parameters of our proposed models based on the data and successfully reproduce the movements and directional trends of the mares.

中文翻译：

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后宫群放牧数学模型

在动物群体中，个体之间的相互作用实现协调运动以保持凝聚力。在后宫群中，放牧是种马从后面追赶母马的行为；它被认为有助于提高群体凝聚力。在放牧期间使用无人机拍摄和视频跟踪的方法研究了群体凝聚力的机制，并根据母马的运动开始时间发现了两个阶段的相互作用。研究表明，最先移动的母马是离公马最近的母马；而较晚的母马的运动开始由与最近的运动母马的距离决定。因此，作为充分理解群体凝聚力的第二步，我们提出了一个由后宫种马放牧的母马的数学模型，这是对放牧期间绵羊模型的修改。我们的模型是五个组成部分的线性组合：惯性、来自种马的排斥、短距离排斥、同步吸引力和对群体中心的吸引力。我们根据数据调整了我们提出的模型的参数，并成功地再现了母马的运动和方向趋势。