Lyapunov exponents from observed time series

Abstract

We examine the question of accurately determining Lyapunov exponents for a time series. We find that it is advantageous to use local mappings with higher-order Taylor series, rather than linear maps as done earlier. We demonstrate this procedure for the Ikeda map and the Lorenz system. We present methods for identifying spurious exponents by analyzing data-set singularities and by determining the Lyapunov direction vectors. The behavior of spurious exponents in the presence of noise is also investigated, and found to be different from that of the true exponents.