Development of nonlinear dynamical analysis for noisy and short time series and application to bio-signals

Abstract

New measures, linear mode complexity(LMC) and divergence in perpendicular recurrence plot(DPRP), which can roughly reflect the main quantities such as the fractional dimension and the largest Lyapunov exponent respectively, are proposed to consider dynamical characteristics of attractor reconstructed from very short time series. These methods are tested with various time series, generated from Lorenz, Roessler and Henon systems. Also their performances are compared with other well-known methods, proper to long chaotic time series. Finally they are applied to a nonstationary simulated signal and an experimental biological signal. Their superiority over other methods requiring tens of thousands of data points in nonlinear dynamics lies in extracting the variations of the fractional dimension and the Lyapunov exponent of phase portrait from a few hundred data points, typically available for biological and other natural systems.