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}] > > ?? > > ____________________________________________________________________________________ Take the Internet to Go: Yahoo!Go puts the Internet in your pocket: mail, news, photos & more. http://mobile.yahoo.com/go?refer=1GNXIC