This paper delves into the flocking behavior of a class of multi-agent systems with symmetrical and asymmetrical delays under hierarchical leadership. First, we present the two corresponding models. Then, mainly using mathematical induction and considering the nature of differential and quadratic functions, we prove that the group can realize flocking with the two types of delays under certain conditions. Finally, we validate the conclusions via numerical simulation results.

中文翻译：

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在具有对称和不对称延迟的等级领导下聚集

本文深入研究了等级领导下一类具有对称和不对称延迟的多智能体系统的集群行为。首先，我们介绍两个相应的模型。然后，主要采用数学归纳法，并考虑微分函数和二次函数的性质，证明了该群在一定条件下可以实现这两种延迟的植绒。最后，我们通过数值模拟结果验证了结论。