Mathematical Biology Seminar Shu Dai MBI, Ohio State University Monday Nov. 16, 2009 3:05pm in LCB 225 Dynamics in the Echebarria-Karma Modulation Equation for Alternans in a Cardiac Fiber Abstract: While alternans in a single cardiac cell appears through a simple period-doubling bifurcation, in extended tissue the exact nature of the bifurcation is unclear. In particular, the phase of alternans can exhibit wave-like spatial dependence, either stationary or travelling, which is known as discordant alternans. We study these phenomena in simple cardiac models through a modulation equation proposed by Echebarria-Karma. We perform a bifurcation analysis for their modulation equation. We also find that for some extreme range of parameters, there are chaotic solutions. Chaotic waves in recent years have been regarded to be closely related to dreadful cardiac arrhythmia. Proceeding work illustrates some chaotic phenomena in two- or three-dimensional space, for instance spiral and scroll waves. We show the existence of chaotic waves in one dimension, which may provide a different mechanism accounting for the instabilities in cardiac dynamics.