  Phase reduction is a general tool widely used to describe forced and
interacting self-sustained oscillators. Here we explore the phase coupling
functions beyond the usual first-order approximation in the strength of the
force. Taking the periodically forced Stuart-Landau oscillator as the
paradigmatic model, we determine and numerically analyse the coupling functions
up to the fourth order in the force strength. We show that the found nonlinear
phase coupling functions can be used for predicting synchronization regions of
the forced oscillator.
