Re: ODEs and phase portraits

*To*: mathgroup at smc.vnet.net*Subject*: [mg14743] Re: ODEs and phase portraits*From*: "Kevin J. McCann" <kevinmccann at Home.com>*Date*: Thu, 12 Nov 1998 02:17:42 -0500*Organization*: @Home Network*References*: <728kp1$ehc@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Try this one: Remove[de] de[epsilon_, x0_, v0_, T_] := Module[{eqn, x, y, t}, eqn = {Derivative[1][Derivative[1][x]][t] + epsilon*(x[t]^2 - 1)* Derivative[1][x][t] + x[t] == 0, x[0] == x0, Derivative[1][x][0] == v0}; y = x /. NDSolve[eqn, x, {t, 0, T}][[1]]; ParametricPlot[{y[t], Derivative[1][y][t]}, {t, 0, T}, PlotStyle -> RGBColor[1, 0, 0], Epilog -> {RGBColor[0, 0, 1], AbsolutePointSize[5], Point[{y[0], Derivative[1][y][0]}]}]; ] Sample usage: de[-.01,1,0,100] If you copy the above into a NB, highlight the bracket, and type Ctl-Shif-N, it will look a lot better. Anyway, try it. Kevin phantomlord at my-dejanews.com wrote in message <728kp1$ehc at smc.vnet.net>... >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 > >