Estimation of Lyapunov Spectra from a Time Series

Nonlinear dynamical systems can be identified by their sensitivity to initial conditions. This is captured by a set of invariant measures called Lyapunov exponents. For accurate estimation of these exponents from an observed time series, we need knowledge of the trajectory representing time evolution of the system attractor. In this paper we present an explanation of reconstructed phase spaces. We then build on the motivation behind Lyapunov exponents and present an algorithm for their estimation. Experiments were performed on two standard chaotic series and on a deterministic, periodic series. Results indicate that positive and zero exponents can be estimated reliably even in the presence of noise