  Magnetic flux ropes play a key role in triggering solar flares in the solar
atmosphere. In this paper, we investigate the evolution of active region NOAA
12268 within 36 hours from 2015 January 29 to 30, during which a flux rope was
formed and three M-class and three C-class flares were triggered without
coronal mass ejections. During the evolution of the active region, the flare
emission seen in the H$\alpha$ and ultraviolet wavebands changed from a
circular shape (plus an adjacent conjugated ribbon and a remote ribbon) to
three relatively straight and parallel ribbons. Based on a series of
reconstructed nonlinear force-free fields, we find sheared or twisted magnetic
field lines and a large-scale quasi-separatrix layer (QSL) associated with 3D
null points in a quadrupolar magnetic field. These features always existed and
constantly evolved during the two days. The twist of the flux rope was
gradually accumulated that eventually led to its instability. Around the flux
rope, there were some topological structures, including a bald patch, a
hyperbolic flux tube and a torus QSL. We discuss how the particular magnetic
structure and its evolution produce the flare emission. In particular, the
bifurcation of the flux rope can explain the transition of the flares from
circular to parallel ribbons. We propose a two-stage evolution of the magnetic
structure and its associated flares. In the first stage, sheared arcades under
the dome-like large-scale QSL were gradually transformed into a flux rope
through magnetic reconnection, which produced the circular ribbon flare. In the
second stage, the flux rope bifurcated to form the three relatively straight
and parallel flare ribbons.
