Bifurcation properties of the two process model.

Daan's two process model is known to be one of the most powerful models, covering various situations from free-running to sleep deprivation. In this study, bifurcation properties of the model dynamics as function of a gap, D, between the threshold processes are clarified using a circle map. As a function of D, we will show that the model has the different types of the mutual entrainment regions that are intervened by the tangent bifurcation. The variable behavior of human circadian rhythm is suggested to be systematically understood based on the bifurcation properties of the two process model.