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

• To: mathgroup at smc.vnet.net
• Subject: [mg81118] Re: help plot log[f[t]] vs a parameter using an ODE
• From: john boy <johnboy98105 at yahoo.com>
• Date: Thu, 13 Sep 2007 06:23:57 -0400 (EDT)

```This causes kernel to crash and close. I'm using
version 5.

Amnd it seems liek you have changed the function to a
PDE instead of an ODe does thatg matter?

What it comes down to is to solve the same ode many
times over the range of a parameter a. (0-40)

But I have hard time understanding how to code up that
part and taking the log of it and plotting the
Log[y[t]] on y axis and then range of a on x axis.

--- Chris  Chiasson <chris.chiasson at gmail.com> wrote:

> On Sep 12, 2:51 am, john <johnboy98... at yahoo.com>
> wrote:
> > 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] == 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.
>
> NDSolve[{D[y[t,a],t]==a (y[t,a]/((y[t,a])^2+b))-c
> y[t,a]
> +d,y[0,a]==0}/.
> {d->0.1,c->1,b->10},y,{t,0,200},{a,1,40}]
>
> ??
>
>

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