The coordinated and ordered collective behavior arising from dispersed and local self-organizing interactions among individuals is widely observed in many biological communities. For populations engaging in group foraging or migration, complex societies with multiple hierarchical levels are common. A prevalent scenario involves two dominant levels, one corresponding to leaders and the other composed of followers. In this paper, we explore how a group can be influenced by a set of leaders to organize and move in a coordinated manner towards a preferred direction. Specifically, we balance social interactions among group members through two weighted factors, corresponding to the leadership and experience of leaders. Through computer simulations, we observe a linear relationship between the proportion of leaders guiding group movement and the group size, with larger groups requiring a higher proportion of leaders while maintaining initial density. Additionally, we identify an optimal leadership interval where group movement performance enhances with increasing leadership up to a certain point, beyond which it starts to decline. Similar patterns are observed concerning individual visual field, indicating the existence of an optimal interval for visual angle. Our findings not only contribute to understanding collective motion in natural biological systems but also provide new insights into effective leadership mechanisms in artificial swarm systems.

中文翻译：

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具有领导力和经验的自推进粒子的集体排队运动


在许多生物群落中，广泛观察到个体之间分散的、局部的自组织相互作用所产生的协调有序的集体行为。对于从事群体觅食或迁徙的人群来说，具有多个等级层次的复杂社会是很常见的。一种普遍的情况涉及两个主导级别，一个对应于领导者，另一个对应于追随者。在本文中，我们探讨了一个群体如何受到一组领导者的影响，以协调的方式组织并朝着首选方向前进。具体来说，我们通过两个加权因素来平衡小组成员之间的社交互动，这两个因素对应于领导者的领导能力和经验。通过计算机模拟，我们观察到引导群体运动的领导者比例与群体规模之间存在线性关系，较大的群体需要更高比例的领导者，同时保持初始密度。此外，我们还确定了一个最佳领导区间，在该区间内，群体运动绩效随着领导力的增加而提高，达到某一点，超过该点则开始下降。在个体视野中观察到类似的模式，表明存在最佳视角区间。我们的研究结果不仅有助于理解自然生物系统中的集体运动，而且还为人工群体系统中的有效领导机制提供了新的见解。