Shu Dai, Department of Mathematics and Center for Nonlinear and Complex Systems, Duke University


Chaos in one-dimensional cardiac models


Abstract: Under rapid periodic pacing, cardiac cells typically undergo a period-doubling bifurcation in which action potentials of short and long duration alternate with one another, which is called alternans. By weakly nonlinear approximation, Echebarria and Karma proposed an amplitude equation to describe the spatiotemporal dynamics of small-amplitude alternans in a class of simple cardiac models on a cardiac fiber. We have computed the spectrum of the linearized operator asymptotically for long cardiac fiber and discussed the bifurcation of the solutions of the amplitude equation. We also found that for some range of the parameters, there exist chaotic solutions, which is 1-dimensional different from those observed in higher dimensions, for instance the spiral waves and scroll waves.

Advisor: David G. Schaeffer (Duke University)