Figure 1.

(A) The motion of a joint over multiple strides is recorded to produce the time series In this case, nearly five strides are shown. For this study, analysis was performed on 104 strides. (B) The embedding dimension is calculated from the False Nearest Neighbors algorithm, detailing the number of time delay copies that are required to accurately represent the attractor. This example shows an embedding dimension of 3 (original plus 2 copies). The time delay (τ) is determined through the Average Mutual Information algorithm. Thus, it is possible to see the original time series (solid), the first delayed copy (dashed line), and the second delayed copy (dotted line). (C) Each of the time series (original plus copies) are plotted against each to provide the state space reconstructed attractor. the above pictured is an example of the ankle angle time series embedded into 3 dimensions for viewing purposes. Actually dimensionality however, may exceed this and is typically around 5 for gait dynamics in healthy individuals. (D) Inset from (C) showing calculation of the largest Lyapunov exponent. A point along a fiduciary trajectory and its true nearest neighbor are selected and the Euclidean distance between these points is calculated (d_t; upper right). These points are then followed along their respective trajectories a certain number of time points (n), followed by distance recalculation (d_t’). The log₂ of the ratio of these distances is calculated and then normalized to the time that the points traversed through the trajectory to yield the Lyapunov exponent.