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Testing Chaotic Dynamics in Systems with Two Positive Lyapunov Exponents: a bootstrap Solution

The present paper is devoted to the problem of detecting the presence of two positive Lyapunov exponents in time series data. In order to accomplish this task the accuracy of the estimates is essential, but existing estimation approaches do not provide it. We present a procedure exploiting resampling methods for building a statistical test for the presence of two positive exponents of comparable magnitudes through rigorous assessment of confidence intervals. The problem is studied by means of computer experiments performed in a variety of conditions on coupled Lorenz systems. Then, a case study regarding the time series of the cardiovascular activity of the toad Bufo Arenarum is presented. A comparison with other estimator algorithms is also shown.