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plot thousands(?) of trajectories in single graph.

hello group, 

I have a routein that solves a system of odes over a
parameter space thousands of times while randomly
varying the values. 

What I would like to do is take a variable and the
resulting solutions(however many routine has generated
over the course of evaluation) and plot them on single

So you will get rather messy graph, but nonetheless
shows possible trajectories given system can yield.

How do I go about doing this? 

I thought i could save the interpolating functions and
then evaluate thousands at the end of a routine and
show together. But How do I save the interpolating

or do I plot with inside the module with
DisplayFunction-> Identity and then save the plot and
DisplayTogether the thousands of graphs at the end of
the routine. 

if doing thousands isn't possible, is it possible to
show hundreds of trajectories? 

thanks in advance for any insights.


code below is a example skeletal code for running
hundred random solutions of an ode system. 

k1 = Random[Real, {1/10, 5/10}];
k2 = Random[Real, {1/20, 5/20}];
ndsolution =
NDSolve[{a'[t] == -k1  a[t] x[t], b'[t] == -k2 b[t]
y[t], x'[t] == -k1 a[t] x[t] + k2 b[t] y[t], y'[t] ==
k1 a[t] x[t] - k2  b[t] y[t], a[0] == 1, b[0] == 1,
x[0] == 1, y[0] == 0},{a, b, x, y}, {t, 0, 250}][[1]];
Plot[Evaluate[{a[t], b[t], x[t], y[t]} /. ndsolution],
{t, 0, 250}, PlotRange -> All, PlotStyle ->
{{AbsoluteThickness[2], RGBColor[0, 0, 0]},
{AbsoluteThickness[2], RGBColor[.7, 0, 0]},
{AbsoluteThickness[2], RGBColor[0, .7, 0]},
{AbsoluteThickness[2], RGBColor[0, 0, .7]}}, Axes ->
False, Frame -> True, PlotLabel -> StyleForm[A
StyleForm[" B", FontColor -> RGBColor[.7, 0, 0]]
StyleForm[" X", FontColor -> RGBColor[0, .7,
0]]StyleForm[" Y", FontColor -> RGBColor[0, 0, .7]],
FontFamily -> "Helvetica", FontWeight -> "Bold"]];
,{i, 100}]

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