Quasiperiodic circus movement in a loop model of cardiac tissue: multistability and low dimensional equivalence

This paper discusses the dynamics of the circus movement around a one-dimensional continuous and uniform loop of model cardiac cells. The membrane ionic currents are represented by a modified Beeler-Reuter formulation. The description of the quasiperiodic regimes initiated in a previous paper is completed and their equivalence with those predicted by an integral-delay model is discussed. The two models differ in the number of quasiperiodic modes of reentry that can be sustained and in the type of bifurcation by which they appear. These differences are the consequences of the modulation of the repolarization phase by diffusion in the ionic model. A modified version of the integral-delay model that includes a spatial averaging in the calculation of the action potential duration is shown to suppress the discrepancies.