Action potential restitution and hysteresis in a reaction-diffusion   system with pacing rate dependent excitation threshold
  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. 
Joseph M. Starobin, Christopher P. Danford, Vivek Varadarajan, Andrei   J. Starobin, Vladimir N. Polotski