### Math Biology Seminar Abstracts

Wednesday September 5, 2001
3:05 pm JWB 208

## Speaker: Eric Cytrynbaum

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

E-mail:
keener@math.utah.edu