Wednesday September 5, 2001 3:05 pm JWB 208
Title: Stability of the traveling pulse and the restitution hypothesis
Abstract - There has been much speculation about the importance of the slope of the restitution curve as a factor in the break-up of spiral waves. The restitution hypothesis claims that stability of a spiral wave relies on the slope of the restitution curve (dAPD/dDI) being less than 1. This hypothesis is the higher dimensional generalization of the stability result of Courtemanche, Keener and Glass (1996). In that paper, the authors show that the under the assumption that the back of the steady traveling pulse is a phase wave, the question of stability reduces to checking the slope of the restitution curve (dAPD/dDI). In this talk, I will present a generalization of the result which assumes that the back of the traveling pulse is propagated (rather than a phase wave). Under this more physiological assumption, it can be shown that stability and the slope of the restitution curve are independent concepts. In particular, it is possible to have a stable pulse even if the slope of the restitution curve is greater than 1. Conversely, an unstable pulse can be associated with a restitution curve whose slope is less than 1.
For more information contact J. Keener, 1-6089