Improved Assessment of Orbital Stability of Rhythmic Motion with Noise
Fig 3
Estimation of a Floquet multiplier (FM) using a new method that estimates the bias of previous methods.
An adjustment calculated based on Burg’s method was added to a first estimate based on the Yule-Walker equation. Time series with different length, n were generated with FM = 0.75 and various distributions of noise: normal (A), uniform (B) and asymmetric lognormal (C). The FM was evaluated for each time series using this new method. The simulation was repeated 1000 times for each n. Compared with the previous methods, the bias is substantially reduced. With this method, H0—the null hypothesis that the estimated orbital stability comes from a distribution with mean equal to the actual value—is accepted when n ≥ 50 for normally or uniformly distributed noise (A and B), and n ≥ 20 for asymmetrically distributed noise (C).