Re: phase portrait

[Arnau Mir Torres]

Hello.

Thanks Peter for the response.
Excuse me but I don't explain correct.
What I need is to plot the solution (x(t),y(t)) of the differential 
equation.
I write the following:

function xdot= f (x, t)
       xdot(1)=x(1)-x(1)^2-x(2)^2;
       xdot(2)=-x(2)+2*x(1)*x(2);
endfunction
x0=[0;1];
t=linspace (0,1.1,200)';
x=lsode("f",x0,t);
for i = 1:length(t)
x1(i)=x(i);
x2(i)=x(length(t)+i);
endfor
gset term postscript
gset output "plot.ps"
plot (x1,x2)

In the previous script, I get  a graph for every initial condition x0 
but I want to plot a lot of graphs in order to obtain how are the 
solutions of the differential system.



Peter Gawthrop wrote:

> Hi Arnau,
>
> try adapting this script. I guess th is x and dth is y in your
> notation. You also need to write fun.m to give dx in terms of x=[th;dth] -
> equivalent to your f&g functions rolled into one.
>
> Peter.
>
>
>  dt = 0.1;
>
>  TH = [-1:0.1:1];
>  DTH = 5*[-1:0.1:1];
>
>  N = length(TH);
>  M = length(DTH);
>
>  i=0;
>  THETA = zeros(N*M,1);
>  DTHETA = zeros(N*M,1);
>  D_THETA = zeros(N*M,1);
>  D_DTHETA = zeros(N*M,1);
>
>  for th=TH
>    for dth=DTH
>      i++;
>      x = [th;dth];
>      dx = fun(x);
>      D_DTHETA(i) =  dx(1);
>      D_THETA(i)  =  dx(2);
>      THETA(i) = th;
>      DTHETA(i) = dth;
>    endfor
>  endfor
>
>
>  M = [THETA DTHETA D_THETA*dt D_DTHETA*dt];
>
>  gset nokey
>  axis([min(TH), max(TH), min(DTH), max(DTH)]);
>  ylabel("$\\dot{\\theta}$")
>  xlabel("$\\theta$")
>  grid on;
>  gplot M with vector
>
>
> From: Arnau Mir Torres <address@hidden>
> Subject: phase portrait
> Date: Mon, 21 Feb 2005 15:36:45 +0100
>
>  
>
> > Hello.
> > I want to plot a phase portrait for a system of differential equations 
> > of the form:
> >
> > xdot= f(t,x,y)
> > ydot= g(t,x,y)
> >
> > where t is the independent variable.
> >
> > I want to plot in the x-y plane coordinates the phase portrait of the 
> > previous differential equation.
> >
> > Somebody can tells me if there exists a package or a script in octave 
> > that does it?
> >
> > Thanks in advance,
> > Arnau.
> >
> >
> > --
> > Arnau Mir Torres
> > Director Departament Matemàtiques i Informàtica.
> > Universitat de les Illes Balearss.
> > Edifici A. Turmeda, Campus de la UIB.
> > Crta. de Valldemossa, km. 7,5.
> > 07122 Palma de Mallorca.
> > Baleares.
> > Spain.
> > Phone: +34 971 172987
> > Fax: +34 971 173003
> > e-mail: address@hidden
> > web: http://dmi.uib.es/~arnau
> >
> >
> >
> > -------------------------------------------------------------
> > Octave is freely available under the terms of the GNU GPL.
> >
> > Octave's home on the web:  http://www.octave.org
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> > -------------------------------------------------------------
> >
> >    
>
>
> -------------------------------------------------------------
> Octave is freely available under the terms of the GNU GPL.
>
> Octave's home on the web:  http://www.octave.org
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>  


--
Arnau Mir Torres
Director Departament Matemàtiques i Informàtica.
Universitat de les Illes Balearss.
Edifici A. Turmeda, Campus de la UIB.
Crta. de Valldemossa, km. 7,5.
07122 Palma de Mallorca.
Baleares.
Spain.
Phone: +34 971 172987
Fax: +34 971 173003
e-mail: address@hidden
web: http://dmi.uib.es/~arnau



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Octave's home on the web:  http://www.octave.org
How to fund new projects:  http://www.octave.org/funding.html
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