Model Mathematics

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Component: environment

Component: r

\frac{d}{d time} (r) = (ract hr Ir - (k6 r)) + Ir2 ract = 1.0 - (\frac{s^{n1}}{s^{n1} + {theta_1}^{n1}}) hr = 1.0 - (\frac{{h_delta1}^{n3}}{{h_delta1}^{n3} + {(j1 theta_3)}^{n3}}) Ir = \{\begin{matrix} 0.0 if time \geq 0.0 \land time ≦ 90.0 \\ 10.0 if time \geq 91.0 \land time ≦ 92.0 \\ 0.0 if time \geq 93.0 \land time ≦ 113.0 \\ 10.0 if time \geq 114.0 \land time ≦ 115.0 \\ 0.0 if time \geq 116.0 \land time ≦ 136.0 \\ 10.0 if time \geq 137.0 \land time ≦ 138.0 \\ 0.0 if time \geq 139.0 \land time ≦ 159.0 \\ 10.0 if time \geq 160.0 \land time ≦ 161.0 \\ 0.0 if time \geq 162.0 \land time ≦ 252.0 \\ 10.0 if time \geq 253.0 \land time ≦ 254.0 \\ 0.0 if time \geq 255.0 \land time ≦ 275.0 \\ 10.0 if time \geq 276.0 \land time ≦ 277.0 \\ 0.0 if time \geq 278.0 \land time ≦ 298.0 \\ 10.0 if time \geq 299.0 \land time ≦ 300.0 \\ 0.0 if time \geq 301.0 \land time ≦ 321.0 \\ 10.0 if time \geq 322.0 \land time ≦ 323.0 \\ 0.0 otherwise \end{matrix} Ir2 = \{\begin{matrix} 0.0 if time \geq 0.0 \land time ≦ 5.0 \\ 1000.0 if time \geq 6.0 \land time ≦ 7.0 \\ 0.0 if time \geq 8.0 \land time ≦ 12.0 \\ 1000.0 if time \geq 13.0 \land time ≦ 14.0 \\ 0.0 if time \geq 15.0 \land time ≦ 21.0 \\ 1000.0 if time \geq 22.0 \land time ≦ 23.0 \\ 0.0 if time \geq 24.0 \land time ≦ 204.0 \\ 1000.0 if time \geq 205.0 \land time ≦ 206.0 \\ 0.0 if time \geq 207.0 \land time ≦ 217.0 \\ 1000.0 if time \geq 218.0 \land time ≦ 219.0 \\ 0.0 if time \geq 220.0 \land time ≦ 227.0 \\ 1000.0 if time \geq 228.0 \land time ≦ 229.0 \\ 0.0 if time \geq 230.0 \land time ≦ 310.0 \\ 1000.0 if time \geq 311.0 \land time ≦ 312.0 \\ 0.0 if time \geq 313.0 \land time ≦ 321.0 \\ 1000.0 if time \geq 322.0 \land time ≦ 323.0 \\ 0.0 otherwise \end{matrix}

Component: s

\frac{d}{d time} (s) = (Is g - (k7 s)) + Is2

Component: se

\frac{d}{d time} (se) = Ise - (k7 se)

Component: f

\frac{d}{d time} (f) = (- (k1 (r + c) f)) + (k2 + k3 phi_b_s) (1.0 - f) phi_b_s = \frac{1.0}{1.0 + ⅇ^{\frac{- (\log_{10} (1.0 (s + se)) - sb)}{delta_b}}}

Component: h

\frac{d}{d time} (h) = j1 ((k4 + k5 (1.0 - phi_r_s)) (r + c) f - (k8 h)) phi_r_s = \frac{1.0}{1.0 + ⅇ^{\frac{- (\log_{10} (1.0 (s + se)) - sr)}{delta_r}}}

Component: g

\frac{d}{d time} (g) = g1 hact \frac{gmax - g}{gmax} - (g2 Is g) hact = \frac{{h_delta}^{n2}}{{h_delta}^{n2} + {(j1 theta_2)}^{n2}}

Component: hh

\frac{d}{d time} (hh) = j1 (Ih - (k8 hh))

Component: model_parameters

h_delta = (h + hh) delta h_delta1 = (h + hh) delta1 Is = \{\begin{matrix} 10.0 if time > 0.0 \land time ≦ 90.0 \\ 0.0 if time > 90.0 \land time ≦ 180.0 \\ 10.0 if time > 180.0 \land time ≦ 270.0 \\ 0.0 if time > 270.0 \land time ≦ 360.0 \\ 0.0 otherwise \end{matrix}