标题： 耦合振荡器网络中高阶相位约化的参数化方法 显示英文标题

标题： A parametrisation method for high-order phase reduction in coupled oscillator networks

摘要： 我们提出了一种用于弱耦合振子网络的高阶相位约简的新方法，更一般地，适用于可约化正常双曲（准）周期环面的扰动。 我们的方法通过计算扰动不变环面的嵌入的渐近展开式，以及局部坐标中的约简相位动力学。 两者都可以以任意精度确定，并且我们证明相位动力学可以直接以标准形式获得。 我们将该方法应用于预测耦合Stuart-Landau振子链中的远距离同步。 显示英文摘要

摘要： We present a novel method for high-order phase reduction in networks of weakly coupled oscillators and, more generally, perturbations of reducible normally hyperbolic (quasi-)periodic tori. Our method works by computing an asymptotic expansion for an embedding of the perturbed invariant torus, as well as for the reduced phase dynamics in local coordinates. Both can be determined to arbitrary degrees of accuracy, and we show that the phase dynamics may directly be obtained in normal form. We apply the method to predict remote synchronisation in a chain of coupled Stuart-Landau oscillators.