Influence of observational noise on the recurrence quantification analysis

In this paper, we estimate the errors due to observational noise on the recurrence quantification analysis (RQA). Based on this estimation, we present ways to minimize these errors. We give a criterion to choose the threshold ε needed for the optimal computation of the recurrence plot (RP). One important point is to show the limits of interpretability of the results of the RQA if it is applied to measured time series. We show that even though the RQA is very susceptible to observational noise, it can yield reliable results for an optimal choice of ε if the noise level is not too high. We apply the results to typical models, such as white noise, the logistic map and the Lorenz system, and to experimental laser data.