Evidence for an unfolded border-collision bifurcation in paced cardiac tissue

TL;DR

This study combines experimental and theoretical approaches to reveal a hybrid bifurcation behavior in paced cardiac tissue, introducing the concept of an unfolded border-collision bifurcation to explain the transition from smooth to border-collision dynamics.

Contribution

The paper introduces the unfolded border-collision bifurcation model, explaining the hybrid bifurcation behavior observed in cardiac tissue experiments.

Findings

Hybrid bifurcation behavior observed experimentally

Near bifurcation point dynamics are smooth-like

Further from bifurcation point dynamics are border-collision-like

Abstract

We investigate, both experimentally and theoretically, the bifurcation to alternans in heart tissue. Previously, this phenomenon has been modeled either as a smooth or as border-collision period-doubling bifurcation. Using a new experimental technique, we find a hybrid behavior: very close to the bifurcation point the dynamics are smooth-like, whereas further away they are border-collision-like. This behavior is captured by a new type of model, called an unfolded border-collision bifurcation.