New Formulation of the Noise Effects in Chaotic Intermittency

Abstract

This chapter is devoted to the noise effect in intermittency. A method to obtain theoretical expressions for the noisy reinjection probability density function is developed, which basically consists in extending the M(x) function technique used in Chap. 5 to derive the noiseless reinjection probability density. Moreover, this methodology allows to study the noise effect on the intermittency statistical properties for relatively large noise strengths. We also derive analytical approximations for other statistical variables, such as the probability density of the laminar lengths and the average laminar length. This methodology can describe the statistical properties of the noiseless system using the noisy data. Also, we show that occasionally the presence of noise could not be detected due to the results that behave as they would be corresponding to a noiseless system.