# PlotRange problems

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 – Dr. 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 – Dr. belisarius Aug 2 '12 at 16:16
By the way, welcome to Mathematica.SE! Please consider registering your account so that any votes you receive on this question can be added to those given on your future questions and answers. This will allow you to do more on the site over time. – Verbeia Aug 2 '12 at 21:28

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}]


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