2007/12/20 by Xiaopeng Zhao, David G. Schaeffer, Zhao, Xiaopeng +8
Computer Science · Medicine · Physics and Astronomy · #Biological Physics (physics.bio-ph) #Cardiac electrophysiology and arrhythmias #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #physics.bio-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.0712.3336
18 pages, 6 figures
arxiv created 2007/12/20 · openalex publication_date 2007/12/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 the 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.