A statistical framework for testing chaotic dynamics via Lyapunov exponents

Abstract One common criticism of the existing Lyapunov exponents algorithms is the absence of a distributional theory which provides a framework for the statistical hypothesis testing for the calculated Lyapunov exponents. This paper presents a methodology to calculate the empirical distributions of Lyapunov exponents by using a bootstrapping technique. The methodology of the paper provides a formal test of chaos under the null hypothesis. The numerical examples show that the method works well with small data sets.

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