Flip-Flip Bifurcation in a Mathematical Cardiac System

Abstract

We study the intersection of double-flip (period-doubling) bifurcations in a parameter plane. We derive normal forms for discrete-time and continuous-time systems. Using these normal forms, we clarify the bifurcation structure around the flip-flip bifurcation point. We apply these analytical results to a system of coupled ventricular cell models. We determine the coexistence of in-phase and anti-phase two-periodic solutions. We make the simplest model for generating discordant alternans and clarify that two parameters (free concentration of potassium ions in the extracellular compartment and the conductance of the gap junction) play key roles in generating discordant alternans.