The dynamics of reentry in a model of a two-dimensional annulus of homogeneous cardiac tissue, with a Beeler-Reuter type formulation of the membrane ionic currents, is examined. The bifurcation structure of the sustained propagated solutions is described as a function of $R_{\mathit{\text{in}}}$ and $R_{\mathit{\text{out}}}$, the inner and outer radii of the annulus. The transition from periodic to quasiperiodic reentry occurs at a critical $R_{\mathit{\text{in}}}$, which first diminishes and then saturates as $R_{\mathit{\text{out}}}$ is increased. The reduction of the critical $R_{\mathit{\text{in}}}$ is a consequence of the increase of the wave-front curvature. There is a range of $R_{\mathit{\text{in}}}$ below the critical radius in which two distinct quasiperiodic solutions coexist. Each of these solutions disappears at its own specific value of $R_{\mathit{\text{in}}}$, and their annihilation is preceded by a new type of bifurcation leading to a regime of propagation with transient successive detachments of the wave front from the inner border of the annulus.

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