  Robust delay induced oscillations, common in nature, are often modeled by
delay-differential equations (DDEs). Motivated by the success of
phase-amplitude reductions for ordinary differential equations with limit cycle
oscillations, there is now a growing interest in the development of analogous
approaches for DDEs to understand their response to external forcing. When
combined with Floquet theory, the fundamental quantities for this reduction are
phase and amplitude response functions. Here, we develop a framework for their
construction that utilises the method of harmonic balance.
