Recent observations indicate that hydrogen-poor superluminous supernovae
often display bumpy declining light curves. However, the cause of these
undulations remains unclear. In this paper, we have improved the magnetar
model, which includes flare activities. We present a systematic analysis of a
well-observed SLSNe-I sample with bumpy light curves in the late-phase. These
SLSNe-I were identified from multiple transient surveys, such as the
Pan-STARRS1 Medium Deep Survey (PS1 MDS) and the Zwicky Transient Facility
(ZTF). Our study provides a set of magnetar-powered model light curve fits for
five SLSNe-I, which accurately reproduce observed light curves using reasonable
physical parameters. By extracting essential characteristics of both explosions
and central engines, these fits provide valuable insights into investigating
their potential association with gamma ray burst engines. We found that the
SLSN flares tend to be the dim and long extension of the GRB flares in the peak
luminosity versus peak time plane. Conducting large-scale, high cadence surveys
in the near future could enhance our comprehension of both SLSN undulation
properties and their potential relationship with GRBs by modeling their light
curve characteristics.Comment: 10 pages, 5 figures. Accepted for publication in the Astrophysical
Journa