J. Hamill

LYAPUNOV EXPONENT ESTIMATION FOR HUMAN GAIT ACCELERATION SIGNALS

While it is not possible to analytically define the Lyapunov exponents for biological systems, estimating the spectrum of exponents or simply the largest exponent is possible. Two algorithms are often used for experimental data: the Wolf algorithm [1] and the Rosenstein algorithm [2]. Rosenstein’s algorithm was developed to address limitations inherent in the Wolf algorithm, including: reliability issues with small data sets, computational intensity, and sensitivity to noise. Wolf and Rosenstein both suggest a minimum of 10 data points for Lyapunov estimation, where d is the dimension of the attractor; however, Rosenstein et al. claim their algorithm performs well with smaller data sets. How well these algorithms perform on small biological data sets (<10) is of interest.