Summary: Low-Frequency Noise Controls On-Off Intermittency of Bifurcating Systems
and Kirone Mallick2
Laboratoire de Physique Statistique, Ecole Normale Supe´rieure, 24 rue Lhomond, 75005 Paris, France
SPhT, Orme des Merisiers, CEA-Saclay, 91191 Gif-sur-Yvette, France
(Received 11 February 2005; published 1 August 2005)
A bifurcating system subject to multiplicative noise can display on-off intermittency. Using a canonical
example, we investigate the extreme sensitivity of the intermittent behavior to the nature of the noise.
Through a perturbative expansion and numerical studies of the probability density function of the unstable
mode, we show that intermittency is controlled by the ratio between the departure from onset and the value
of the noise spectrum at zero frequency. Reducing the noise spectrum at zero frequency shrinks the
intermittency regime drastically. This effect also modifies the distribution of the duration that the system
spends in the off phase. Mechanisms and applications to more complex bifurcating systems are discussed.
DOI: 10.1103/PhysRevLett.95.064101 PACS numbers: 05.45.2a, 47.15.2x
Among the possible behaviors of a chaotic system is
intermittent behavior. The system remains for long dura-
tions in some regular state (say a laminar state or off-phase)