How to extract Lyapunov exponents from short and noisy time series

In this correspondence, we discuss an algorithm for the extraction of Lyapunov spectra from short and noisy time series. Initially, we briefly describe an existing algorithm and include a method for improving the robustness to noise of this algorithm. The problem of short time series is then addressed, and a novel concatenation technique is presented and combined with the extraction algorithm previously utilized. Results of applying this extended algorithm to chaotic time series are presented, and the effects of noise and data length are discussed.