Re: Re: phase-space versus controlling parameter surface

• To: mathgroup at smc.vnet.net
• Subject: [mg91783] Re: [mg91737] Re: phase-space versus controlling parameter surface
• From: danl at wolfram.com
• Date: Sun, 7 Sep 2008 22:54:08 -0400 (EDT)
• References: <200809070933.FAA25419@smc.vnet.net>

```> Dear All,
>
> I am interested in plotting a surface of the phase-space versus a
> controlling parameter, e.g. the B in a Duffing's equation
>
> x'[t] == v[t]
> v'[t] == - x[t]^3 - k v[t] + B Cos[t]
>
> that is, in the space {x[t], v[t], B} for a known k and B varying from
> Bmin to Bmax
> I tryed something like :
>
> ParametricPlot3D[ Evaluate[{x[t], v[t], B} /. NDSolve[{v'[t] == - x[t]^3 -
> k v[t] + B Cos[t], x'[t] == v[t], x[0] == 1, v[0] == 0}, {x=, v}, {t, 0,
> 2000}, MaxSteps -> Infinity] ], {t, 1950, 1950 + 4 Pi}, {B, 0.2, 0.6}]
>
> but without success.
> Is there any way to get it ?
>
> Thank you very much for your help.
>
> Yours,
> Luca P.
> Milano - Italy
>
> (I re-edited the message, I had some problem with 7-bit... sorry..)
>

There are probably better ways, but you can do a list plot provided you
first specify a value for k. Here is an example.

k = .3;

Clear[g];
g[b_?NumberQ] :=
g[b] = {x[t], v[t], b} /. First[NDSolve[{x'[t] == v[t] ,
v'[t] == -x[t]^3 - k*v[t] + b*Cos[t], x[0] == 1, v[0] == 0}, {x,
v}, {t, 0, 2000}, MaxSteps -> Infinity]]

pts = Table[
Evaluate[Table[g[b], {b, 0.2, 0.6, .01}]], {t, 1950, 2000}];

Now do:

ListPlot3D[Flatten[pts, 1]]

What I obtained can best be described as the proverbial kitchen sink.

Daniel Lichtblau
Wolfram Research

```

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