ODEs and phase portraits

*To*: mathgroup at smc.vnet.net*Subject*: [mg14708] ODEs and phase portraits*From*: phantomlord at my-dejanews.com*Date*: Tue, 10 Nov 1998 01:21:01 -0500*Organization*: Deja News - The Leader in Internet Discussion*Sender*: owner-wri-mathgroup at wolfram.com

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 -----------== Posted via Deja News, The Discussion Network ==---------- http://www.dejanews.com/ Search, Read, Discuss, or Start Your Own