MMA绘制非线性微分方程组的解

青青子衿

1. eqns = {D[S[t], t] ==
2.     10 - 0.8 S[
3.        t]*\[ScriptCapitalI][t]/(S[t] + \[ScriptCapitalI][t]) -
4.      0.8 S[t],
5.    D[\[ScriptCapitalI][t], t] ==
6.     0.8 S[t]*\[ScriptCapitalI][t]/(S[t] + \[ScriptCapitalI][t]) -
7.      0.75 \[ScriptCapitalI][t],
8.    D[Q[t], t] == 0.4 \[ScriptCapitalI][t] - 0.2 Q[t],
9.    D[R[t], t] ==
10.     0.7 S[t] + 0.25 \[ScriptCapitalI][t] + 0.1 Q[t] - 0.1 R[t],
11.    S[0] == 50, \[ScriptCapitalI][0] == 20, Q[0] == 10, R[0] == 20};
12. sol = NDSolveValue[eqns, {S, \[ScriptCapitalI], Q, R}, {t, 0, 30}];
13. ParametricPlot[{{t, sol[[1]][t]}, {t, sol[[2]][t]}, {t,
14.    sol[[3]][t]}, {t, sol[[4]][t]}}, {t, 0, 40}, AspectRatio -> 6/7,
15. ImageSize -> Large,
16. PlotLegends ->
17.   Placed[LineLegend[{"S(t)", "I(t)", "Q(t)", "R(t)"},
18.     LegendFunction -> (Framed[#, RoundingRadius -> 5] &),
19.     LegendMargins -> 5], {1.0, 0.9}],
20. PlotStyle -> {Red, Blue, Green, Purple}]

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