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Fixed points for system using PlotVectorField
*To*: mathgroup at smc.vnet.net
*Subject*: [mg62720] Fixed points for system using PlotVectorField
*From*: "Diana" <diana.mecumxiii at sbcglobal.remove13.net>
*Date*: Fri, 2 Dec 2005 05:53:27 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
Math folks,
I am trying to determine the fixed points of the following system:
dx/dt = x(1-x^2-y^2)
dy/dt = y(2-x^4-y^4)
I understand that you study
dy/dx = y(2-x^4-y^4)/x(1-x^2-y^2) and see what happens to the field when
dx/dt and dy/dt = 0.
I would like to know if I am using the PlotVectorField function in the
correct way.
What I coded was the following:
PlotVectorField[{1, y(2-x^4-y^4)/x(1-x^2-y^2)},{x,-2,2},{y,-2,2},Axes ->
Automatic]
My plot shows a fixed point at (1.18921, 0), which is the (fourth root of 2,
0).
This makes sense, as one of the solutions for x...
Solve[y(2-x^4-y^4)==0, x] is the fourth root of 2.
What I don't understand is the following:
There seem to be other points of interest on the plot at the following
points: (+/- 1.16, +/- 0.7)
When I search for x's and y's close to one another computationally which
make y(2-x^4-y^4)/x(1-x^2-y^2 -> 0, I get (+/- 0.6, +/- 0.8).
Can someone tell me if I am applying the PlotVectorField appropriately, and
if so, how I should interpret the points of interest on the plot?
Thanks,
Diana
--
=====================================================
"God made the integers, all else is the work of man."
L. Kronecker, Jahresber. DMV 2, S. 19.
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