Figure 1

Schematic representations of dependent measure calculations. A: Example of mean ± 1 SD for a typical time series. Between-stride standard deviations are computed at each % of the gait cycle (i) and then averaged to compute the MeanSD across the entire gait cycle (Eq. 2). B: An original time series, q(t), is reconstruction into a 3-dimensional attractor such that S(t) = [q(t), q(t+T), q(t+2T)]. The two triplets of points indicated in A and separated by time lags T and 2T each map onto a single point in the 3D state space. C: Expanded view of a local section of the attractor shown in B. An initial naturally occurring local perturbation, d _j (0), diverges across i time steps as measured by d _j (i). The average logarithmic divergence, <d _j (i)> is computed across all pairs of initially neighboring trajectories and then fit with a double exponential function (Eq. 5). D: Representation of a Poincaré section transecting the state space perpendicular to the system trajectory. The system state at stride k, S _k , evolves to S_k+1one stride later. The Floquet multipliers quantify whether the distances between these states and the system fixed point, S*, grow or decay across multiple strides (Eq. 8).