We present constants of motion for the finite-dimensional Lohe type aggregation models with frustration, and apply them to the analysis of collective behaviors. The Lohe type models have been proposed as possible non-abelian and higher-dimensional generalizations of the Kuramoto model, which is a prototype phase model for synchronization. In this paper, we study the emergent collective dynamics of these models under the effect of (interaction) frustration, which generalizes phase-shift frustrations in the Kuramoto model. To this end, we provide constants of motion, i.e., conserved quantities along the flow generated by the models under consideration. From the perspective of the low-dimensional dynamics, we derive several results on the emergent asymptotic patterns of the Kuramoto and Lohe sphere models.

我们给出了带有挫折感的有限维Lohe型聚集模型的运动常数，并将其应用于集体行为的分析。已经提出将Lohe类型模型作为Kuramoto模型的可能的非阿贝尔和更高维度的概括，Kuramoto模型是用于同步的原型阶段模型。在本文中，我们研究了在（交互）挫折感的影响下这些模型的新兴集体动力学，它概括了仓本模型中的相移挫折感。为此，我们提供运动常数，即沿所考虑的模型生成的流的守恒量。从低维动力学的角度，我们得出了关于仓本和乐河球体模型的渐近渐近模式的几个结果。