Delay Coordinates Method for Estimating the Largest Lyapunov Exponent

Lyapunov exponents are widely used quantifiers for characterising regimes in dynamical systems. Within this perspective, the improvement and methodological optimisation to estimate the dynamic characteriser of the largest Lyapunov exponent is necessary. Over the decades, several researchers in the field of dynamical systems and statistical physics have dedicated themselves to this task. This effort culminated in the development of Wolf’s algorithm, which was presented as a very robust and accurate method, but costly and difficult to understand methodologically. In order to overcome these problems, Sato, and later Rosenstein, based on the conservation of phase space through canonical transforms of phase space, used the method of delayed coordinates to estimate in the reconstructed phase space through a time serie of the system to estimate in a practical way the largest Lyapunov exponent.Thus, this article aims to describe the characteristics of the method of delayed coordinates for the estimation of the largest Lyapunov exponent, and to evaluate its quality for this task.

Keywords:
Lyapunov Exponent; Delay Coordinates; Logistic Map