Papers Published

1. X. Zhao and D. G. Schaeffer and C. M. Berger and W. Krassowska and D. J. Gauthier, Cardiac Alternans Arising From an Unfolded Border-Collision Bifurcation, Journal Of Computational And Nonlinear Dynamics, vol. 3 no. 4 (October, 2008) .
   (last updated on 2009/09/02)

   Abstract:
   Following an electrical stimulus, the transmembrane voltage of cardiac tissue rises rapidly anti 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 alternans exhibits hybrid smooth/nonsmooth 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 bifurcation parameter providing guidance for the development of future models. [DOI: 10.1115/1.2960467]