The time series of ac conductivities at 2 kHz along the direction (represented as the c2-axis) perpendicular to the c-axis of an ytterbium nitrate crystal is measured at low temperatures above 11 K but below 50 K in both the cooling and heating processes. Bursts are observed in the time series of the conductivities. Singularities are found in the properties of the fluctuations of the conductivities near 32 K in the cooling process and near 41 K in the heating process.