Stability conditions for the traveling pulse: Modifying the restitution hypothesis

As a simple model of reentry, we use a general FitzHugh-Nagumo model on a ring (in the singular limit) to build an understanding of the scope of the restitution hypothesis. It has already been shown that for a traveling pulse solution with a phase wave back, the restitution hypothesis gives the correct stability condition. We generalize this analysis to include the possibility of a pulse with a triggered wave back. Calculating the linear stability condition for such a system, we find that the restitution hypothesis, which depends only on action potential duration restitution, can be extended to a more general condition that includes dependence on conduction velocity restitution as well as two other parameters. This extension amounts to unfolding the original bifurcation described in the phase wave back case which was originally understood to be a degenerate bifurcation. In addition, we demonstrate that dependence of stability on the slope of the restitution curve can be significantly modified by the sensitivity to other parameters (including conduction velocity restitution). We provide an example in which the traveling pulse is stable despite a steep restitution curve. (C) 2002 American Institute of Physics.