Publications [#246411] of Daniel J Gauthier

Papers Published
  1. Zhao, X; Schaeffer, DG; Berger, CM; Krassowska, W; Gauthier, DJ, Cardiac alternans arising from an unfolded border-collision bifurcation, Journal of Computational and Nonlinear Dynamics, vol. 3 no. 4 (2008), pp. 223-232 [Gateway.cgi], [doi] .

    Following an electrical stimulus, the transmembrane voltage of cardiac tissue rises rapidly and remains at a constant value before returning to the resting value, a phenomenon known as an action potential. When the pacing rate of a periodic train of stimuli is increased above a critical value, the action potential undergoes a period-doubling bifurcation, where the resulting alternation of the action potential duration is known as alternans in medical literature. Existing cardiac models treat alternans either as a smooth or as a border-collision bifurcation. However, recent experiments in paced cardiac tissue reveal that the bifurcation to altemans exhibits hybrid smooth/honsmooth behaviors, which can be qualitatively described by a model of so-called unfolded border-collision bifurcation. In this paper we obtain analytical solutions of the unfolded border-collision model and use it to explore the crossover between smooth and nonsmooth behaviors. Our analysis shows that the hybrid smooth/nonsmooth behavior is due to large variations in the system's properties over a small interval of the biurcation parameter, providing guidance for the development of future models. Copyright © 2008 by ASME.