Locating Separatrices and Basins of Stability in Biodynamic Systems

In biomechanics, a separatrix or recovery envelope exists between standing and falling. Standing with postural sway is a distinctly different type of motion than falling. A comparable problem to standing postural sway is the challenge of maintaining torso stability. In this case, a separatrix exists delineating stable torso sway from unstable and potentially injurious motion. An approach is presented for identifying separatrices in state space generated from noisy time series data sets representative of those generated from experiments. We demonstrate how Lagrangian coherent structures (LCS), ridges in the state space distribution of finite-time Lyapunov exponents (FTLE), can be used to locate these separatrices. As opposed to previous approaches which required an entire vector field, this method can be performed using a single trajectory that evolves over time.