Restitution Function
Pitchfork Bifurcation

(Click inside the applet to start)

The restitution function is a mesoscopic characteristic of cardiac tissue. It characterizes the duration of an action potential (APD, which is the time the cell is in an excited state) as a function of the preceding diastolic interval (DI, which is the time the cell is in an unexcited state). Compared to the previous restitution function applet, the difference here is that the lower plot shows the action potentials produced as a function of the pacing period.

To use the applet, click in the applet to give an initial pacing period and find the resulting APD and DI. Then, while continuing to press the mouse button, drag to move over a range of periods. The resulting APDs are plotted in the lower plot as a function of period. By moving over different values, the bifurcation diagram takes shape in the lower plot. This diagram indicates a single value of APD at long periods, with the creation of a multi-valued function (two APDs) at shorter periods that correspond to alternans.

In this case, alternans is produced by a pitchfork bifurcation. Observe the way in which the alternans "opens up" as the cycle length is decreased past the critical period for the onset of alternans and compare with the border-collision bifurcation.