Chapter 9: The Role of the Noise in the Chaotic Intermittency

DEL RIO, EZEQUIEL; ELASKAR, SERGIO

Recent Trends in Chaotic, Nonlinear and Complex Dynamics

World Scientific

Año: 2021; p. 193 - 226

Intermittency is a particular route to the deterministic chaos character-ized by spontaneous transitions between laminar and chaotic dynamics.The classical theory of intermittency was firstly introduced by Pomeauand Manneville in the context of the Lorenz system. Later, the classicaltheory was extended into a new intermittency theory that includes thosecases that produce statistic behavior far from the classical predictions.This chapter is devoted to the additive noise effect in the mapsthat have intermittency. From classical point of view, two approachesaddressing this problem are the most important ones: Fokker?Planckand renormalization group analysis. Both cases only consider the noiseeffect in the local map, that is, near to the unstable point where thelaminar behavior takes place. Later, in a paper with Prof. Miguel A. F.Sanjuán the noise effect on the new intermittency theory was consideredand it was shown that the noise on the chaotic region also affects thestatistical dynamics in the laminar region. It has also been found goodagreement between the new proposed noise theory and the numericalsimulations. Recently, experimental evidences on the new intermittencytheory have been found in continuous systems. The noise effect has alsobeen investigated in these systems and some differences with theorypredictions have been found hence open questions remain for futureinvestigations.