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3d phase spacesurface 
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#1
Feb2713, 11:58 PM

P: 234

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 ndimensional curve in a ndimensional 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
Feb2813, 04:39 PM

HW Helper
Thanks
P: 1,004

It may be possible for the solution curve to be dense on some surface. 


#3
Mar413, 02:52 AM

P: 234

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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