FIGURE 4.

A geometrical decomposition of state sensitivity into path-dependent and -independent parts. A perturbation in a parameter can change the state trajectory, whose magnitude and direction are given by the state sensitivity as shown in the left figure (dashed arrow). This difference consists of two parts as magnified in the right figure; the first is a path-dependent change causing the phase shift Δφ (dotted arrow perpendicular to the isochron), and the second is a path-independent portion along the isochron. Note that the path-dependent phase change is equivalent to