Figure 1.

Schematic Representation of State-space Construction. (A) The original time series of raw data define the states (q₁, q₂, …) of the system. (B) These states are combined to form the system’s trajectory in state space (only a 3-dimensional state space is shown here used for illustrative purposes). (C) Expanded view of a typical local region. A small perturbation moves the system at S(t) to its closest neighbor S(t*). Local divergence is computed by measuring the Euclidean distances between the subsequent points, denoted d_j(i). The local dynamic stability of the system is defined by how quickly, on average, the two trajectories diverge away from each other. Rates of divergence, λ*_S and λ*_L, were calculated from the slopes of the mean log divergence curve (Eq. 2). (D) Poincaré sections are defined to be orthogonal to the mean (i.e., limit) cycle. The system state, S_k, at stride k evolves to S_k+1 one stride later. Floquet multipliers quantify, on average, whether the distances between these states and the system fixed point, S*, grow or decay after one cycle (Eq. 5).