The Role of the Noise in the Chaotic Intermittency

Abstract

Intermittency is a particular route to the deterministic chaos characterized by spontaneous transitions between laminar and chaotic dynamics. The classical theory of intermittency was firstly introduced by Pomeau and Manneville in the context of the Lorenz system. Later, the classical theory was extended into a new intermittency theory that includes those cases that produce statistic behavior far from the classical predictions. This chapter is devoted to the additive noise effect in the maps that have intermittency. From classical point of view, two approaches addressing this problem are the most important ones: Fokker–Planck and renormalization group analysis. Both cases only consider the noise effect in the local map, that is, near to the unstable point where the laminar behavior takes place. Later, in a paper with Prof. Miguel A. F. Sanjuán the noise effect on the new intermittency theory was considered and it was shown that the noise on the chaotic region also affects the statistical dynamics in the laminar region. It has also been found good agreement between the new proposed noise theory and the numerical simulations. Recently, experimental evidences on the new intermittency theory have been found in continuous systems. The noise effect has also been investigated in these systems and some differences with theory predictions have been found hence open questions remain for future investigations.