Phase response function ($Y^{\prime }=-DF(U{)}^{\mathsf{T}}Y$)

A periodic phase response function describes the first-order phase shift produced by a perturbation along a limit cycle. With period-one orbit $U$, choose the periodic adjoint solution normalized by ${\int }_0^{1}Y\cdot U^{\prime }ds=1$. The Fredholm solvability condition then projects forcing $p$ to ${\int }_0^{1}Y\cdot pds$. For voltage-difference coupling, the averaged interaction is $h(\varphi )={\int }_0^1{Y}^1(s)U^1(s+\varphi )ds$.