Singularities in the fluctuation of on-off intermittency

For a two-dimensional piecewise linear map exhibiting on-off intermittency, the scaling property of fluctuation, i.e., the large deviation property is investigated. It is shown that there are three phases of fluctuation and the q-weighted average of an observed quantity has singularities such as jumps or a plateau due to transitions between the phases. At the onset of on-off intermittency, the width of the plateau vanishes due to the disappearance of one of the three phases and the singularity becomes weaker but more probable. The singularity at the onset of on-off intermittency is also examined on the coupled logistic map.