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Re: ODEs and phase portraits

  • To: mathgroup at
  • Subject: [mg14728] Re: ODEs and phase portraits
  • From: Selwyn Hollis <shollis at>
  • Date: Wed, 11 Nov 1998 17:53:34 -0500
  • Organization: fair
  • References: <728kp1$>
  • Sender: owner-wri-mathgroup at

Dear 'lord,

This should help:

    f[epsilon_][x_,y_]:= -epsilon(x^2-1)y-x

        {x'[t]==y[t], y'[t]==f[epsilon][x[t],y[t]],  x[0]==x0, y[0]==y0}







phantomlord at wrote:

> I am trying to write a function such that I have the following ODE:
> x''(t)+epsilon*(x(t)^2-1)*x'(t)+x(t)==0  [1] where epsilon is to be one
> of the parameters in the function. I want to beable to draw out the
> phase portraits for the equation for different values of epsilon.
> To deduce the phase portraits in a mathematical procedure I multiply
> equation[1] by dx(t)/dt and integrate w.r.t. t.  To do this in
> Mathematica is trivial, so I'll skip past this - it is the next step
> that I would like assistance with:
> Q:Is there a way that I can decompose the result of the above (I'll call
> it [2]) into the corresponding pair (below) of ODEs to deduce the
> trajectory of the phase portrait?
> x'(t) = y(t)
> y'(t) = f(x,y)
> some f(x,y) function of x and y.
> Perhaps there is a built in function that will allow me to do this? If
> not do, can anybody suggest another way to do this?
> Also after plotting the trajectory is there any way to determine the
> direction of it in Mathematica?
> thanks for you time.
> Paul
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Dr. Selwyn Hollis
Associate Professor of Mathematics
Armstrong Atlantic State University
Savannah, GA 31419 USA

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