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3d phase space-surface

  1. Feb 27, 2013 #1
    Is it possible for a surface to be obtained as the solution for a system of differential equations in a 3d phase space?
    Almost all 3d phase plots I have observed are curves,example the Lorenz system.

    Is there a general formula that says that a system of n differential equations would produce a n-dimensional curve in a n-dimensional phase space?

    Problem at hand:
    I have been provided the individual 2d solution plots for a 3 variable,2 parameter system.Now,with these 2d solution plots,I want to make the 3d phase plot.In the process,I also want to create a system of 3 differential equations.Any suggestions?
  2. jcsd
  3. Feb 28, 2013 #2


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    The solution of a 3D (ordinary) differential equation is a function from the reals to [itex]\mathbb{R}^3[/itex], in other words a curve (or a fixed point). If there is a conserved quantity, then the solution curve must lie on a surface on which that quantity is constant, but it's still a curve.

    It may be possible for the solution curve to be dense on some surface.
  4. Mar 4, 2013 #3
    My problem is a math modelling problem.It is a system of 3 variables and I have been provided 2 solution curve graphs for 1 variable with another.(X vs Y, Y vs Z). I am to now arrive at a 3 eq autonomous system differential equation w.r.t time i.e dX/dt,dY/dt,dZ/dt.
    To top all of this complexity,one of my solution graphs is a set of implicit functions(inverse parabola).
    So,I would like finally want to arrive at a 3system autonomous d.e and plot the solution curve and hope that it is dense enough to form a surface(another constraint).
    I am struggling to go from the solution curves to the autonomous case.Suggestions/helpful keywords in context would help greatly.
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