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.