We report results on the timing analysis of the 2020 giant outburst of 1A 0535+262, using broadband data from Insight-HXMT. The analysis of the pulse profile evolution from the subcritical-luminosity to the supercritical-luminosity regime is presented for the first time. We found that the observed pulse profile exhibits a complex dependence on both energy and luminosity. A dip structure at the energy of the cyclotron resonant scattering features is found for the first time in the pulse fraction–energy relation of 1A 0535+262, when the outburst evolves in a luminosity range from 4.8 × 1037 to 1.0 × 1038 erg s−1. The observed structure is luminosity dependent and appears around the source critical luminosity (∼6.7 × 1037 erg s−1).

We investigate systematically four outbursts of black hole system GX 339-4 observed by the Rossi X-ray Timing Explorer (RXTE) in both spectral and timing domains and find that these outbursts have some common properties, although they experience different ‘q’ tracks in the hardness–intensity diagram (HID). While the spectral indices are around 1.5 in the low/hard state (LHS) and 2.4 in the soft intermediate state (SIMS) and high/soft state (HSS), the spectral parameters of thermal, non-thermal, and reflection components vary significantly in transitions from the LHS to HIMS. Also, the quasi-periodic oscillation (QPO) shows a peculiar behaviour during the state transition between the LHS and HIMS: the RMS drop of the type C fundamental QPO is accompanied by the appearance of the second harmonic. Interestingly, the QPO RMS is found to have a similar linear relationship with the non-thermal fraction of emission in different outbursts. These findings provide more clues to aid our understanding of the outbursts of a black hole X-ray binary system.