Math @ Duke

Publications [#150136] of Shu Dai
Papers Submitted
 S. Dai and D. G. Schaeffer, Bifurcations in a modulation equation for alternans in a cardiac fiber,
Math. Modelling and Num. Analysis
(2008) [PDF]
(last updated on 2008/10/31)
Abstract: While alternans in a single cardiac cell appears through a simple perioddoubling bifurcation, in extended tissue the exact nature of the bifurcation is unclear. In particular, the phase of alternans can exhibit wavelike spatial dependence, either
stationary or traveling, which is known as discordant alternans. We study these phenomena in simple cardiac models through a modulation equation proposed by EchebarriaKarma. As
shown in our previous paper, the zero solution of their equation
may lose stability, as the pacing rate is increased, through either a Hopf or steadystate bifurcation. Which bifurcation
occurs first depends on parameters in the equation, and for one critical case both modes bifurcate together at a degenerate
(codimension 2) bifurcation. For parameters close to the degenerate case, we investigate the competition between modes, both numerically and analytically. We find that at sufficiently rapid pacing (but assuming a 1:1 response is maintained), steady patterns always emerge as the only stable solution. However, in the parameter range where Hopf bifurcation occurs first, the evolution from periodic solution (just after the bifurcation) to the eventual standing wave solution occurs through an interesting
series of secondary bifurcations.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

