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Trouble determining the correct direction errors for nullclines

  1. Jun 28, 2004 #1
    I have a simple question regarding nullclines, as I'm having trouble determining the correct direction errors.

    For example, here's a system of equations:

    dx/dt = 2-x-y

    dy/dt=y-x^2

    x-null is y= -x + 2
    y-null is y= x^2

    x-null is vertical, y-null goes horizontal.

    But when I divide the graph in different sections, and pick different plot points which equations do I plug into to find directions?

    I know that wasn't clear, but for example:

    If I want to know if on the y-null if the direction of a certain section is pointing left or right, would I plug the points I chose in:

    A) dy/dt = y-X^2
    B) dx/dt=2-x-y

    or C) y=x^2

    I'm not sure which equation to plug it in. I've tried to think it out, but I end up always confusing myself. Please point me in the right direction. Thanks.
     
  2. jcsd
  3. Jun 29, 2004 #2

    HallsofIvy

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    If I understand correctly what you are doing, away from the "null clines" (pointswhere they intersect are equilibrium points) you would calculate dx/dt and dy/dt at the point then divide (dy/dt)/(dx/dt) to get the slope.
     
  4. Jun 29, 2004 #3
    I'm not sure if that quite helps, I want to know when I take some sample points, which equations do I plug them into in order to get the correct direction.
     
  5. Jun 30, 2004 #4

    HallsofIvy

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    If that is not given by the slope, (dy/dt)/(dx/dt) then I don't know what you want.
     
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