Noise robust estimates of the largest Lyapunov exponent

A first-order correction of the exponential divergence of trajectories in state space of a chaotic time series with noise was proposed. We demonstrated the performance for various examples using data from the Hénon map, Ikeda map and logistic map, which were contaminated with noise. It was found that the proposed method provided a reasonable estimate of the largest Lyapunov exponent even when the noise level was as high as 30% of the signal content. The new method was not sensitive to the distribution of the noise. Furthermore, the comparison with Wolf et al. algorithm showed that our method is much better when dealing with the time series contaminated with noise. Our algorithm was also valid for more complicated chaotic dynamical systems, such as Lorenz attractor and Rössler-hyperchaos attractor.