Figure 7

Phases of the Koopman eigenfunctions estimated by row-type Hankel DMD on the conventional coordinative structures. Phases computed as the argument of the Koopman eigenfunctions estimated by row-type Hankel DMD are shown for each walking speed and five harmonic frequencies of a participant. Horizontal and vertical axes are principal axes extracted by SVD-based method. For clarity, we aligned the initial phases to near-zero values by the time-shift for all eigenfunctions. All trajectories rotate clock-wise from the black dots. Although the shapes were similar among various velocities, the changes in the phase with walking speed (or gait cycles) were inhomogeneous. For example, the phases visually advanced with the increase of the walking speed, such as in the boundary between blue and red at the bottom in the plots of ω₁ (but the phase did not seemingly change in the boundary between red and yellow).