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MathGroup Archive 2007

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81130] Re: help plot log[f[t]] vs a parameter using an ODE
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Thu, 13 Sep 2007 06:30:15 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <fc85qt$liu$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

and

LogPlot[y[t] /. ksol[[1]], {t, 0, 40}, PlotRange -> All]

will not do that ? but in you post, it is not clear
what do you mean by "while varying a over a range
 > of values ( 0-40)" ..

Regards
   Jens

john 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.
> 
> 


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