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MathGroup Archive 2004

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Re: plot thousands(?) of trajectories in single graph.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50494] Re: plot thousands(?) of trajectories in single graph.
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 8 Sep 2004 05:08:27 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <chk0es$so$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

DoRandomSolution[i_Integer] :=
  Block[{$DisplayFunction = Identity, sol},
    Table[sol = NDSolve[{
              y''[t] - g*y'[t] + (1 + Cos[omega*t])*y[t] == 0,
              y[0] == Random[], 
              y'[0] == Random[]} /.
            {g -> Random[], 
              omega -> 2Pi*Random[]}, {y[t]}, {t, 0, 6Pi}];
      Plot[Evaluate[y[t] /. sol[[1]]], {t, 0, 2Pi}], {i}]
    ]

ss = DoRandomSolution[4000];
Show[ss]

Regards
  Jens


sean kim wrote:
> 
> 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
> graph.
> 
> 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
> function?
> 
> 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.
> 
> sean
> 
> code below is a example skeletal code for running
> hundred random solutions of an ode system.
> 
> Do[
> Module[{},
> 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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