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We present a novel method for high-order phase reduction in networks ofweakly coupled oscillators and, more generally, perturbations of reduciblenormally hyperbolic (quasi-)periodic tori. Our method works by computing anasymptotic expansion for an embedding of the perturbed invariant torus, as wellas for the reduced phase dynamics in local coordinates. Both can be determinedto arbitrary degrees of accuracy, and we show that the phase dynamics maydirectly be obtained in normal form. We apply the method to predict remotesynchronisation in a chain of coupled Stuart-Landau oscillators.

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