Testing for Chaos in Deterministic Systems with Noise
By Georg A. Gottwald, Ian Melbourne. 2004
301 citations recorded by the source corpus.
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 method” 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.
Subfields: Computer Networks and Communications, Economics and Econometrics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/926de61fdbf06ab4c2d4991ea1e87e6d85e7d560
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Citations in the corpus
- The Lyapunov Characteristic Exponents and Their Computation (2008, methodology): “In the category of methods based on the analysis of a time series constructed by the coordinates of the orbit under study, one may list the frequency map analysis of Laskar [83, 86, 84, 85], the “0–1” test [64, 65], the method of the low-frequency spectral analysis [137, 81], the “patterns method” [”
- On the validity of the 0–1 test for chaos (2009, methodology): “We first recall the simplified form of the test proposed in [6].”
- On the Implementation of the 0-1 Test for Chaos (2009, methodology): “Recently we have introduced a binary test for chaos, the 0–1 test, designed for the analysis of deterministic dynamical systems [8, 9].”