Distinct small-distance scaling behavior of on-off intermittency in chaotic dynamical systems

On-off intermittency in chaotic dynamical systems refers to the situation where some dynamical variables exhibit two distinct states in their course of time evolution. One is the ''off'' state, where the variables remain approximately a constant, and the other is the ''on'' state, when the variables temporarily burst out of the off state. Previous work demonstrates that there appears to be a universal scaling behavior for on-off intermittency. In particular, the length of off time intervals, or the length of the laminar phase, obeys the algebraic scaling law. We present evidence that there are in fact distinct classes of on-off intermittency. Although the statistics of their laminar phase obeys the algebraic scaling, quantities such as the average transient time for trajectories to fall in a small neighborhood of the asymptotic off state exhibit qualitatively different scaling behaviors. The dynamical origin for producing these distinct classes of on-off intermittency is elucidated.