       help plot log[f[t]] vs a parameter using an ODE

• To: mathgroup at smc.vnet.net
• Subject: [mg81096] help plot log[f[t]] vs a parameter using an ODE
• From: john <johnboy98105 at yahoo.com>
• Date: Wed, 12 Sep 2007 03:47:26 -0400 (EDT)

```I've solved the following equation for y[t].

eqn = y'[t] == a (y[t]/((y[t])^2 + b )) - c y[t] + d

keqn = eqn /. {a -> 10 , d -> 0.1 , c -> 1 , b -> 10 }

ksol = NDSolve[{keqn, y == 0}, y, {t, 0, 200}]

Plot[y[t] /. ksol, {t, 0, 200}, PlotRange -> All];

Now I would like to plot the log of y[t] while varying a over a range
of values ( 0-40)

How will I accomplish this?  It seems like I would have to solve the
DE while varying a a little at a time then take the log of it?

At first I thought the following will do the trick, but it didn't. I
was trygin to make varying parameter a into a function x[t] by using
interpolation.

{{x -> Interpolation[Range[0, 40]]}}

then

ParametricPlot[y[t], x[t], {t, 0, 200}]

generates

ParametricPlot::pllim: Range specification x[t] is not of the form {x,
xmin, xmax}

I'm trying to find the value of y[t] as a parameter a incerases from
0  to 40.

When the Log[y[t]] is plotted against parameter over the range of 0 to
40, that should show bistability.

Except y[t] will change as you vary a. and Log[y[t]] will change along
with it.

Thanks for any input.

```

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