# Oscillations exist when the response is steep and the time delay is long enough.

A) Steady state response of APC/C to Cdk1 activity. Higher *m* corresponds to a steeper response. B) When Cdk1 is suddenly activated, APC/C follows after a fixed time in the model with one discrete delay. C) Phase diagram for parameters and *τ*, for different values of *m*. Increasing *m* corresponds to an larger region of oscillations. D) Fixed point location. The dots show the APC/C activity in steady state, for different *c*. The fixed point can be found as the intersection of the APC/C response curve and the dashed lines, which are derived by putting the right hand side of Eq (1) to zero. E) Phase diagram for parameters *m* and *τ*, with period in color. The points correspond to parameter values used for the timeseries in G and H. F) Phase diagram for parameters *k*_{s}/*K* and *b*_{deg} with period in color. G) Time series (sinusoidal) for *m* and *τ* denoted by point G. H) Time series (relaxation-like) for *m* and *τ* denoted by point H. Other parameters for G and H: *k*_{s} = 1.28 nM/min, *b*_{deg} = 0.1 min^{−1}. I) The two timeseries from G and H plotted in a plane. Note that APC/C is not an independent variable, but is a time-delayed function of Cdk1. The dashed line denotes the steady-state reponse of APC/C to Cdk1. The oscillations occur around the threshold value.