lrz = {
x'[t] == -3 (x[t] - y[t]),
y'[t] == -x[t] * z[t] + 26 * x[t] - y[t],
z'[t] == x[t] * y[t] - z[t] };
ParametricPlot3D [
Evaluate[{x[t], y[t], z[t]} /.
NDSolve[{lrz, x[0] == 5, y[0] == 0, z[0] == 25}, {x, y, z}, {t, 0, 100}]],
{t, 0, 100},
PlotRange -> {{-25, 25}, {-25, 25}, {0, 50}}, Boxed -> False,
ColorFunction -> {Hue[#4, 1., 0.9] &}, PlotStyle -> Thickness[.0015],
PlotPoints -> 200 ]
(кликабельно)
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