Characterization of on-off intermittency

Abstract

The recently reported behavior known as ‘‘on-off intermittency’’ [N. Platt, E. A. Spiegel, and C. Tresser, Phys. Rev. Lett. 70, 279 (1993)] is investigated in a class of one-dimensional maps that are multiplicatively coupled to either random or chaotic signals. Specific attention is paid to the conditions for the onset of intermittent behavior, the distribution of laminar phases, and the mean laminar phase as a function of the coupling strength. An exact expression is obtained for the distribution of laminar phases in the case of uniformly distributed random driving. A universal asymptotic -3/2 power-law distribution is proven to hold for a large class of random driving cases. Power-law scaling of the mean laminar phase as a function of coupling strength near onset is predicted for random driving, with a critical exponent of -1. Numerical studies with chaotically driven maps reveal similar behavior to random driving cases and suggest the need for a systematic study of ‘‘chaotic walks.’’