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Math Help - Lotka-Volterra equations

  1. #1
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    Lotka-Volterra equations

    I have two first order differential equations of the following:

    x'=pxy - qx
    y'=rxy - sy

    These two equations are meant to mimic two interacting populations.

    Is it possible to rearrange them into the Lotka-Volterra equations to solve them for equilibrium points?

    this would give:

    x'=px(1 - y/Y)

    y'=-ry(1 - x/X)

    cheers
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by thermalwarrior View Post
    I have two first order differential equations of the following:

    x'=pxy - qx
    y'=rxy - sy
    x'=-qx(1-(p/q)y)
    y'=-sy(1-(r/s)x)

    So put Y=q/p and X=s/r for the equilibrium populations

    RonL
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  3. #3
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    so was my rearrangement wrong?

    Just im writing this out by hand showing my working and not sure if my working is correct
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by thermalwarrior View Post
    so was my rearrangement wrong?

    Just im writing this out by hand showing my working and not sure if my working is correct
    You seemed to have gotten the p's and q's mixed up. But the solution I gave is the equilibrium (steady state solution) for the original coupled system you gave (its just the solution of x'=y'=0)

    RonL
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  5. #5
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    x'=-qx(1 - Y/y)

    y'=-sy(1 - X/x)

    with equilibrium points at (0,0), (X,Y) ????
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  6. #6
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    [IMG]file:///C:/DOCUME%7E1/Paul/LOCALS%7E1/Temp/moz-screenshot-2.jpg[/IMG][IMG]file:///C:/DOCUME%7E1/Paul/LOCALS%7E1/Temp/moz-screenshot-3.jpg[/IMG][IMG]file:///C:/DOCUME%7E1/Paul/LOCALS%7E1/Temp/moz-screenshot-4.jpg[/IMG]also I have a computer question related to this question:

    this is bit im having a problem with:

    i need to enter into the program u(x,y).

    u(x,y) = dx/dt where x(t) = [x(t) y(t)]^T

    is it the equations from earlier in the question? or do I have to change the form of them???
    cheers
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