Model Mathematics

\frac{d}{d time} (x) = \{\begin{matrix} \frac{a1}{k1 + y} - (b1 x) if time \geq 0.0 \land time < 10000.0 \\ (\frac{a1}{k1 + y} - (b1 x)) + kp if time \geq 10000.0 \land time < 10360.0 \\ \frac{a1}{k1 + y} - (b1 x) if time \geq 10360.0 \land time < 11440.0 \\ (\frac{a1}{k1 + y} - (b1 x)) + kp if time \geq 11440.0 \land time < 11800.0 \\ \frac{a1}{k1 + y} - (b1 x) if time \geq 11800.0 \land time < 12880.0 \\ (\frac{a1}{k1 + y} - (b1 x)) + kp if time \geq 12880.0 \land time < 13240.0 \\ \frac{a1}{k1 + y} - (b1 x) if time \geq 13240.0 \land time < 14320.0 \\ (\frac{a1}{k1 + y} - (b1 x)) + kp if time \geq 14320.0 \land time < 14680.0 \\ \frac{a1}{k1 + y} - (b1 x) if time \geq 14680.0 \land time < 15760.0 \\ (\frac{a1}{k1 + y} - (b1 x)) + kp if time \geq 15760.0 \land time < 16120.0 \end{matrix}

\frac{d}{d time} (y) = epsilon (\frac{(a2 + a3 x) y z}{k2 + x^{2.0}} - (b2 y))

\frac{d}{d time} (z) = epsilon delta (a4 x - (\frac{a5 x z}{k3 + x} + b3 z))