The mobile agents’ circular formation problem is driven by applications that require a desired spatial and temporal separation, such as data collection or satellite constellations. There are numerous strategies to assign the cluster number and spacing, the radius of the trajectory, communication network, and other parameters. In this numerical study, we are particularly interested in the effects of time-delay and phase lag on circular formations with symmetric clusters in a first-order model with all-to-all interaction. When the information exchange time-delay exceeds some critical value, it leads to either incoherent or alternative symmetric arrangements. Besides, we show that formations can be effectively controlled using phase lags. As a paradigmatic example, we consider identical phase lags for half of the agents, while the other half receives an opposite phase lag. As a result, the system reaches more complicated stable arrangements. For instance, the agents can split into asymmetric clusters, each of them creating a symmetric formation.

移动代理的圆形编队问题是由需要所需空间和时间分离的应用程序驱动的，例如数据收集或卫星星座。有许多策略可以分配集群数量和间距、轨迹半径、通信网络和其他参数。在这项数值研究中，我们对时间延迟和相位滞后对具有全方位相互作用的一阶模型中对称簇的圆形地层的影响特别感兴趣。当信息交换时延超过某个临界值时，会导致不连贯或替代的对称安排。此外，我们表明可以使用相位滞后有效地控制地层。作为一个典型的例子，我们考虑一半代理的相同相位滞后，而另一半接收到相反的相位滞后。结果，系统达到更复杂的稳定布置。例如，代理可以分成不对称的集群，每个集群都创建一个对称的结构。