标题： 球面上相同振子的同步：外部力和高阶相互作用下的精确结果 显示英文标题

标题： Synchronization of identical oscillators on a sphere: exact results with external forces and higher-order interactions

摘要： 我们研究了在高阶相互作用和外部周期力作用下，Kuramoto模型在球面上的动力学。 对于相同的振子，我们引入了一种新颖的方法，将三体和四体相互作用纳入序参量的动力学中，从而实现了该系统的完全降维。 我们讨论了这种降维如何以两种不同方式实现以及它们之间的关系。 当限制在赤道上时，动力学与通常的Kuramoto模型相似，只是耦合常数有一个有趣的重新归一化。 在该平面之外，运动简化为两个参数的一组周期轨道。 我们还定位了系统作为不同参数函数的分歧曲线。 显示英文摘要

摘要： We study the dynamics of the Kuramoto model on the sphere under higher-order interactions and an external periodic force. For identical oscillators, we introduce a novel way to incorporate three- and four-body interactions into the dynamics of the order parameter, allowing for a full dimensional reduction of this system. We discuss how such reduction can be implemented in two different ways and how they are related. When restricted to the equator, the dynamics is similar to that of the usual Kuramoto model, up to an interesting renormalization of the coupling constants. Outside this plane, the motion reduces to a two-parameter set of periodic orbits. We also locate the bifurcation curves of the system as functions of different parameters.