Re: phase portrait

[Paul Laub]

Dear Arnau, 

I am not sure I understand your question, but the
answer might be simple. Consider these commands 

>> [tt, xx]  = ode45('vdpol', [0 200], [1 1] );

where [1 1] are the initial conditions, and 0 to 200 is
the range of tt (time). 

# phase space where time is implicit
>> plot( xx(:,1), xx(:,2), 'o');

# below, time is the independent variable 
>> plot( tt, xx(:,1), 'o');
>> plot( tt, xx(:,2), 'o');

In this example, ode45 is an ODE integrator. One such
program is available at 
    http://octave.sourceforge.net/index/index.html
Search on the letter "O" and look for "ode45". 
"vdpol" names an M-file that is written
as follows. 

    # vdpol.m
    function xdot = vdpol(t, x)
        xdot    = zeros(2,1);
        xdot(1) = x(2);
        xdot(2) = 2 * (1 - x(1).^2) .* x(2) - x(1);
    endfunction

You can replace the Vanderpol equation with your own
ODE system. You will likely have to use your own
(different) parameters for ode45 

Paul Laub 



On Mon, 21 Feb 2005 17:40:23 +0100, Arnau Mir Torres <address@hidden> wrote:
> 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
> >>
> >>
> >>
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> >>
> >>Octave's home on the web:  http://www.octave.org
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> >>
> >>
> >
> >
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> >Octave is freely available under the terms of the GNU GPL.
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> >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
> 
> -------------------------------------------------------------
> Octave is freely available under the terms of the GNU GPL.
> 
> Octave's home on the web:  http://www.octave.org
> How to fund new projects:  http://www.octave.org/funding.html
> Subscription information:  http://www.octave.org/archive.html
> -------------------------------------------------------------
> 
>



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