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电梯直达

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发表于 2020-3-24 15:32 |只看该作者 |正序浏览

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Clear[Am, As, Aa, \[Alpha], \[Rho], \[Theta]m, \[Theta]s, \
\[CurlyPhi]m, \[CurlyPhi]s, \[Epsilon]]
\[Gamma]a = 0.1; \[Gamma]m = 0.15; \[Gamma]s =
1 - \[Gamma]a - \[Gamma]m;
\[Epsilon] = 0.04; \[Alpha] = 0.3; \[Rho] = 0.04;
\[Theta]m = 0.75; \[Theta]s = 0.9;
gRate = 0.02;
Am = (gRate + \[Rho])/\[Alpha]; Ba = 4; Bm = 1; Bs = 2.5;
ps = Bm/Bs; pa = Bm/Ba;
\[Delta] = 0.03;
B = \!\(TraditionalForm\`\*
FractionBox[
RowBox[{
RowBox[{
RowBox[{
StyleBox["(",
SpanMinSize->1.,
SpanMaxSize->1.],
RowBox[{"1", "\[Minus]", "\[Alpha]"}],
StyleBox[")",
SpanMinSize->1.,
SpanMaxSize->1.]}], "gRate"}], "+", "\[Rho]"}],
   "\[Alpha]"] \[Minus] \[Delta]\);
cap = 10;
csp = (pa*cap)/ps;
D = ((1 \[Minus] \[Alpha])*
gRate + \[Rho] - \[Alpha]*\[Delta])/(\[Rho] + gRate);
\[CurlyPhi]m = 0.1; \[CurlyPhi]s = 0.1;
Print["*** Initial Values ***"]
E0 = 1.5;
K0 = E0/B;
hm0 = 0.25; hs0 = 0.25;(* initial values *)
\[Eta]m0 = hm0/K0; \[Eta]s0 = hs0/K0;
xm0 = (B*\[Gamma]m^\[Epsilon]*
hm0^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
   hs0^\[Theta]s)^(1 - \[Epsilon]));
xs0 = (B*\[Gamma]s^\[Epsilon]*(ps*
   hs0^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(
1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
   hs0^\[Theta]s)^(1 - \[Epsilon]));
Print["\[Eta]_{m,0}=" <> ToString[\[Eta]m0],
", \[Eta]_{s,0}=" <> ToString[\[Eta]s0],
", x_{m,0}=" <> ToString[xm0], ", x_{s,0}=" <> ToString[xs0]]
TT = 100;(* end time *)
(* Solve differential equations *)
Sol = NDSolve[{xs'[t] = (1 - \[Epsilon])*
   xs[t]*( (1 - xs[t]/
      B)*(\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 1) -
      xm[t]/B \[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1))),
xm'[t] == (1 - \[Epsilon])*
   xm[t]*( (1 - xm[t]/
      B)*\[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1) -
   xs[t]/B*\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) -
      1) ), \[Eta]m'[
   t] == \[CurlyPhi]m*
   xm[t] - (\[CurlyPhi]m + gRate)*\[Eta]m[t], \[Eta]s'[
   t] == \[CurlyPhi]s*xs[t]/ps - (\[CurlyPhi]s + gRate)*\[Eta]s[t],
K'[t] == gRate*K[t], hm[t] == \[Eta]m[t]*K[t],
hs[t] == \[Eta]s[t]*K[t],
Sa[t] == (\[Gamma]a^\[Epsilon]*(pa)^(1 - \[Epsilon]))/(\[Gamma]a^\
\[Epsilon]*pa^(1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
   hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
      hs[t]^\[Theta]s)^(1 - \[Epsilon])) + (\[Gamma]m^\[Epsilon]*
   hm[t]^(\[Theta]m*(1 - \[Epsilon]))*pa*
   cap)/((\[Gamma]a^\[Epsilon]*pa^(
      1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
      hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*
   xm (t)),
Sm[t] == (\[Gamma]m^\[Epsilon]*
   hm[t]^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(
   1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
   hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
      hs[t]^\[Theta]s)^(1 - \[Epsilon])),
Ss[t] == (\[Gamma]s^\[Epsilon]*(ps*
      hs[t]^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(
   1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
   hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
      hs[t]^\[Theta]s)^(1 - \[Epsilon])) - (\[Gamma]m^\[Epsilon]*
   hm[t]^(\[Theta]m*(1 - \[Epsilon]))*ps*
   csp)/((\[Gamma]a^\[Epsilon]*pa^(
      1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
      hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*
   xm (t)), xm[0] == xm0,
xs[0] == xs0, \[Eta]m[0] == \[Eta]m0, \[Eta]s[0] == \[Eta]s0,
K[0] == K0}, {xm, xs, \[Eta]m, \[Eta]s, K, hm, hs, Sa, Sm, Ss}, {t,
0, TT}]
Plot[{Evaluate[Sa[t] /. Sol], Evaluate[Sm[t] /. Sol],
  Evaluate[Ss[t] /. Sol]}, {t, 0, TT}, AxesOrigin -> {0, 0},
PlotRange -> {0., 0.8}, PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
Plot[{Evaluate[D*Sa[t] /. Sol],
  Evaluate[(D*Sm[t] + (\[Alpha]*(gRate + \[Delta]))/(\[Rho] +
   gRate)) /. Sol], Evaluate[D*Ss[t] /. Sol]}, {t, 0, TT},
AxesOrigin -> {0, 0}, PlotRange -> {0., 0.8},
PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]

Set::wrsym: Symbol D is Protected.

NDSolve::deqn: Equation or list of equations expected instead of 0.96 (1-6.66667 xs[t]) xs[t] (-0.5 xm[t] (-1+xm[t]/\[Eta]m[t])+0.09 (-1+(2.5 xs[t])/\[Eta]s[t])) in the first argument {0.96 (1-6.66667 xs[t]) xs[t] (-0.5 xm[t] (-1+xm[t]/\[Eta]m[<<1>>])+0.09 (-1+(2.5 xs[t])/\[Eta]s[<<1>>])),<<13>>,K[0]==10.}.

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