  We have demonstrated that rate dependent restitution and action potential
duration-refractory period hysteresis can be reproduced in a one-dimensional
two-variable Chernyak-Starobin-Cohen reaction-diffusion medium with variable
excitation threshold. We show that restitution and hysteresis depend on the
relationship between pacing period and steady state excitation threshold and
also on the rate of excitation threshold adaptation after an abrupt change in
pacing period. It was also observed that the onset of action potential duration
alternans is determined by the minimal stable wavefront speed, which could be
approximated by the analytical critical speed of a stable solitary pulse. This
approximation was suitably accurate regardless of the adaptation constant of
excitation threshold, its dependence on pacing interval, or magnitude of the
slopes of restitution curves.
