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Math Help - Rikitake model

  1. #1
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    Rikitake model

    for the system

    dx/dt= -vx+zy
    dy/dt= -vy+(z-a)x
    dz/dt= 1-xy

    a,v are positive parameter.

    after finding the fixed points, how am i supposed to classify them??
    Should I build a 3*3 matrix??
    If so, how am I supposed to take derivative, cuz there are non-linear turms like zy and xy????????????????

    Thanks
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  2. #2
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    Quote Originally Posted by felixmcgrady View Post
    for the system

    dx/dt= -vx+zy
    dy/dt= -vy+(z-a)x
    dz/dt= 1-xy

    a,v are positive parameter.

    after finding the fixed points, how am i supposed to classify them??
    Should I build a 3*3 matrix??
    If so, how am I supposed to take derivative, cuz there are non-linear turms like zy and xy????????????????

    Thanks
    Yes, your 3X3 matrix is the Jacobian matrix. Sub in your critical points and then look at the eigenvalues of the matrix, this will give you the stablility of the critical point.
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