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.
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