Applied Math

Duke Applied Mathematics

Publications [#244118] of David G. Schaeffer

Papers Published

  1. Berger, CM; Zhao, X; Schaeffer, DG; Dobrovolny, HM; Krassowska, W; Gauthier, DJ, Period-doubling bifurcation to alternans in paced cardiac tissue: crossover from smooth to border-collision characteristics., Physical Review Letters, vol. 99 no. 5 (2007), pp. 058101, ISSN 0031-9007 [17930795], [doi]
    (last updated on 2018/02/18)

    We investigate, both experimentally and theoretically, the period-doubling bifurcation to alternans in heart tissue. Previously, this phenomenon has been modeled with either smooth or border-collision dynamics. Using a modification of existing experimental techniques, we find a hybrid behavior: Very close to the bifurcation point, the dynamics is smooth, whereas further away it is border-collision-like. The essence of this behavior is captured by a model that exhibits what we call an unfolded border-collision bifurcation. This new model elucidates that, in an experiment, where only a limited number of data points can be measured, the smooth behavior of the bifurcation can easily be missed.

Duke University * Arts & Sciences * Mathematics * February 18, 2018

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