Multistability of reentrant rhythms in an ionic model of a two-dimensional annulus of cardiac tissue

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_in and R_out, the inner and outer radii of the annulus. The transition from periodic to quasiperiodic reentry occurs at a critical R_in, which first diminishes and then saturates as R_out is increased. The reduction of the critical R_in is a consequence of the increase of the wave-front curvature. There is a range of R_in below the critical radius in which two distinct quasiperiodic solutions coexist. Each of these solutions disappears at its own specific value of R_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.