Abstract
The quenching of alternans exhibited as solutions of a cardiac conduction model is considered. The model consists of a nonlinear discrete-time piecewise smooth system, and was previously used to show a link between cardiac alternans and period doubling bifurcation. In this work, it is first shown that the model indeed admits a period doubling border collision bifurcation, and that it is this bifurcation that leads to the alternan solutions. No smooth period doubling bifurcation occurs in the parameter region of interest. Next, recent results of the authors on feedback control of border collision bifurcation are applied to the model, resulting in quenching of the period doubling border collision bifurcation and hence in alternan suppression.
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