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

*To*: mathgroup at smc.vnet.net*Subject*: [mg81110] Re: help plot log[f[t]] vs a parameter using an ODE*From*: Chris Chiasson <chris.chiasson at gmail.com>*Date*: Thu, 13 Sep 2007 06:19:47 -0400 (EDT)*References*: <fc85qt$liu$1@smc.vnet.net>

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}] ??