Analysis Seminar

Speaker: Irina Popovici, US Naval Academy

Abstract: The talk addresses the bifurcations of a two-dimensional non-linear dynamical system introduced by Kline and Baker to model cardiac rhythmic response to periodic stimulation. The dynamical behavior of this continuous (but only piece-wise smooth) model transitions from simple (a unique attracting cycle) to complicated (co-existence of stable cycles) as the stimulus period is decreased from large towards zero.

The first bifurcation, of discontinuous period-doubling type, results from the collision of two cycles with a switching manifold. For stimuli periods just shorter than collision time, of the two cycles about to collide, the 2:1 escalator is stable and the alternans solution is unstable; with those co-exists a stable 1-escalator whose orbit lays away from the switching manifold. The resulting dynamical systems associated with these collisions are being described for some classes of parameters.