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MathGroup Archive 2008

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phase-space versus controlling parameter surface

  • To: mathgroup at smc.vnet.net
  • Subject: [mg91726] phase-space versus controlling parameter surface
  • From: Luca Petrone <luke-sky-walker at hotmail.it>
  • Date: Sat, 6 Sep 2008 02:09:51 -0400 (EDT)

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=2C in the space {x[t]=2C v[t]=2C B} for a known k and B varying from Bmin to BmaxI tryed something like :

ParametricPlot3D[ Evaluate[{x[t]=2C v[t]=2C B} /.    NDSolve[{v'[t] == - x[t]^3 - k v[t] + B Cos[t]=2C            x'[t] == v[t]=2C x[0] ===
 1=2C v[0] == 0}=2C {x=2C v}=2C {t=2C 0=2C 2000}=2C     MaxSteps -> Infinity]  ]=2C {t=2C 1950=2C 1950 + 4 Pi}=2C {B=2C 0.2=2C 0.6}]

but without success.Is there any way to get it ?
Thank you very much for your help.

Yours=2C
Luca P.Milano - Italy
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