标题： Kuramoto模型具有任意阶数的非对称高阶相互作用的精确解 显示英文标题

标题： Exact solutions of the Kuramoto model with asymmetric higher order interactions of arbitrary order

摘要： 高阶相互作用可能导致由Kuramoto模型描述的耦合振子系统中出现新的平衡状态和分岔。 然而，即使在三体相互作用的最简单情况下，根据物体如何耦合，也存在多种可能的函数形式。 这些形式中哪一种更适合描述振子的动力学，取决于所考虑的具体系统。 在这里，我们展示了对于一类特定的相互作用，可以为任意多的物体推导出Kuramoto序参数的简化方程。 此外，给定项对简化方程的贡献并不取决于其阶数，而是取决于我们定义的一种有效阶数。 我们给出了具体的例子，在这些例子中发现了双稳态和三稳态，并讨论了一些奇特的情况，在这些情况下同步是通过三级相变发生的。 显示英文摘要

摘要： Higher order interactions can lead to new equilibrium states and bifurcations in systems of coupled oscillators described by the Kuramoto model. However, even in the simplest case of 3-body interactions there are more than one possible functional forms, depending on how exactly the bodies are coupled. Which of these forms is better suited to describe the dynamics of the oscillators depends on the specific system under consideration. Here we show that, for a particular class of interactions, reduced equations for the Kuramoto order parameter can be derived for arbitrarily many bodies. Moreover, the contribution of a given term to the reduced equation does not depend on its order, but on a certain effective order, that we define. We give explicit examples where bi and tri-stability is found and discuss a few exotic cases where synchronization happens via a third order phase transition.