The next two Constraint equations state that water and sugar are necessary for survival. We model the impact of insufficient water and sugar on both the division rate of the yeast and the average lifetime of the Yeast. The new model (yeast3.mdl) looks like:
The equations are available with the sample model. Note that the Test Inputs chosen cause extreme conditions to exist for Water and Sugar, and the way the model is formulated makes terminations skyrocket. Using Euler integration, the system becomes a 1 period oscillator with Yeast Count going negative. To prevent this, another integration technique can be used, or the equation for terminations changed to:
| terminations = MIN(Yeast Count/TIME STEP, |
| Yeast Count/average lifetime) |
This formulation prevents uninteresting dynamics, but also can set Yeast Count to precisely zero. This means that average sugar and average water need to be computed as
average sugar = ZIDZ(Sugar,Yeast Count)
average water = ZIDZ(Water,Yeast Count)
to prevent a numerical error (overflow) when Yeast Count is 0.
With the changed structure, the model now passes four out of the six Constraints.
