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I have a Delay Differential Equation of the form:

model =  NDSolve[{B'[t] == 562.86 B[t - 2.5] (1 - B[t - 2.5]/(2 10^9)) - 0.3 B[t],
  B[t /; t <= 1950] == 1100000000}, B, {t, 1950, 1970}]; 
plot = Plot[B[t] /. logistic[[1]], {t, 1950, 1970}]

If I put All as input to PlotRange for my graph, no graph appears: it seems there is a limit as to the range of function values that can be displayed in a Mathematica graph. What is this limit?

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Shouldn't it be Plot[B[t] /. model[[1]], {t, 1950, 1970}]? –  J. M. Aug 2 '12 at 16:03
@J.M. Yes, I also think this is a candidate for LogPlot or similar –  belisarius Aug 2 '12 at 16:08
You may try Show[Plot[-Log[-Evaluate[B[t] /. model]], {t, 1952, 1970}], Plot[Log[Evaluate[B[t] /. model]], {t, 1950, 1952}]] to see what is happening –  belisarius Aug 2 '12 at 16:16
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1 Answer

The answer is that there is a problem with your model. Before about 1952.5, it is growing sub-exponentially. Then it suddenly collapses.

plot = LogPlot[B[t] /. model[[1]], {t, 1950, 1970}]

enter image description here

Because the values go negative, it is not even possible to use LogPlot to reveal these data.

Table[B[i] /. model[[1]], {i, 1954, 1960}]

{-1.58056*10^16, -5.51783*10^16, -1.22106*10^24, -9.09786*10^25, \
-1.52099*10^36, -7.66399*10^42, -5.88856*10^45}

belisarius' suggestion, to use Plot[-Log[-Evaluate[B[t] /. model]], {t, 1952, 1970}] to see what is going on, is a good one.

Mathematica is probably refusing to draw the plot when PlotRange->All because it can't come up with a sensible set of ticks / divisions to capture a function that exponentiates like that.

Judging by the size of the units you are using, I am going to guess that this is an attempt at an economic model using GDP or some other quantity measured in the billions and trillions. If so, I would suggest carefully examining the parameters to make sure you haven't slipped a few zeros somewhere. In particular, the parameters $562.86$ seems way too big to generate a sensible non-explosive system.

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Thank you all very much for your help. –  standrewsigem Aug 3 '12 at 9:27
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