Noise effect on statistical properties of type-I intermittency

In this work we analyze the noise effect on type-I intermittency, for which we develop a methodology based on a recently proposed technique used to model the reinjection probability density (RPD). This new methodology allows us to study the noise effect on the intermittency statistical properties for relatively large noise strengths in a quadratic map with different reinjection mechanisms. We show that this procedure allows to predict the behavior of the noisy and noiseless system using the results of the M(x) function which is implemented to obtain the RPD function. We also derive an analytical approximation for the probability density of the laminar lengths and we obtain results for the average laminar length. All analytical approaches show a good agreement with the numerical results even though the statistical properties are calculated using either the noisy or noiseless data, however in some cases the description of the noiseless system using the noisy data can be inaccurate. In addition, we show that occasionally the presence of noise could be not detected due to the results behave as they would be corresponding to a noiseless system. This aspect may have important consequences especially when working with experimental data.