We combine the velocity alignment and aggregation mechanisms to study the collective motion of active agents in noisy circumstances. The agents are located on a two-dimensional square plane, and the proportion of velocity alignment and aggregation interactions are, respectively, set to be $k$ and $1-k$. In the case of $k=1$ our model is similar to the classical Vicsek model, while it degenerates to the view angle model for $k=0$. By tuning the intensity of the external noise $\eta$ and the proportional coefficient $k$, and carrying out extensive numerical simulations, we find that the system can exhibit diverse dynamic patterns widely observed in real biological systems. By means of finite-size scaling analysis, we confirm that the presence of the aggregation interaction affects not only the position of the critical noise ${\eta }_c$ (beyond which the agents display disordered motion) but also the type of the phase transition of the collective motion. In particular, under a weak external noise environment, the transition from disordered to ordered state by increasing $k$ (i.e., by decreasing the proportion of aggregation interaction) is found to be of first order. Besides, for moderate external noise, we also find the existence of the optimal proportion of the aggregation interaction for the system to achieve the highest degree of order. Our results highlights the important role of the aggregation interaction in the collective motion and may have promising potential applications in natural self-propelled particles and artificial multiagent systems.

中文翻译：

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具有速度对齐和聚集交互作用的自推进代理的集体运动模式

我们结合速度对准和聚集机制来研究在嘈杂环境下活性剂的集体运动。代理位于二维正方形平面上，速度对齐和聚集相互作用的比例分别设置为$ķ$ 和 $\mathrm{1个}-ķ$。如果是$ķ=\mathrm{1个}$ 我们的模型类似于经典的Vicsek模型，但退化为 $ķ=0$。通过调整外部噪声的强度$\eta$ 和比例系数 $ķ$，并进行了广泛的数值模拟，我们发现该系统可以展现出在实际生物系统中广泛观察到的多种动态模式。通过有限尺寸缩放分析，我们确认聚集相互作用的存在不仅影响临界噪声的位置${\eta }_C$（除此之外，特工会显示无序运动）以及集体运动的相变类型。特别是在弱外部噪声环境下，通过增加噪声从无序状态到有序状态的转换$ķ$（即，通过减少聚集相互作用的比例）被发现是一阶的。此外，对于适度的外部噪声，我们还发现存在最佳比例的聚集交互作用，以使系统达到最高有序度。我们的结果突出了聚集相互作用在集体运动中的重要作用，并且在自然自推进颗粒和人工多剂系统中可能具有潜在的应用前景。