“…To implement the adaptive phase-amplitude reduction framework, suppose that ( 9) has a nominal parameter set p 0 that describes the dynamics of an underlying model. It is then possible to rewrite (9) as ẋ = F (x, p) + U e (t, p, x), (11) with the extended input U e (t, p, x) ≡ U (t) + F (x, p 0 ) − F (x, p). Intuitively, the term F (x, p) represents dynamics of the model when using parameter set p, and U e captures both the externally applied input and the mismatch caused when considering the parameter set p as compared to the parameter set p 0 of the underlying model (9).…”