Physica D 212 (2005) 100-110.
Georg Gottwald and Ian Melbourne
Abstract
Recently, we introduced a new test for distinguishing regular from chaotic dynamics in deterministic dynamical systems and argued that the test had certain advantages over the traditional test for chaos using the maximal Lyapunov exponent.
In this paper, we investigate the capability of the test to cope with
moderate amounts of noisy data. Comparisons are made between
an improved version of our test and both the ``tangent space''
and ``direct method'' for computing the maximal Lyapunov exponent.
The evidence of numerical experiments, ranging from the logistic map
to an eight-dimensional Lorenz system of differential equations
(the Lorenz 96 system), suggests that our method is superior to
tangent space methods and that it compares very favourably with direct methods.