Phase models with explicit time delays

Studying weakly connected oscillators leads to phase models. It has been proven recently that weakly connected oscillators with delayed interactions do not lead to phase models with time delays even when the delay is of the same order of magnitude as the period of oscillation. This has resulted in a fading interest in such models. We prove here that if the interaction delay between weakly connected oscillators is much longer than the period of oscillation, then the corresponding phase model does have an explicit time delay.