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System of iterated equations

  1. Sep 28, 2011 #1
    The following came up in the context of a genetics question. With the convention that a-e on the LHS have subscript _n+1 and on the RHS a-e have subscript _n,

    a = 2ad + bd
    b = 2ae + bd + be + 2cd + ce
    c = be + ce
    d = 2ad + 2ae + bd + be + ce
    e = bd + be + 2cd + ce

    If the initial values for the variables is a=b=d=e=1, c=0 does the ratio
    e/(a+b+c+d+e) converge as n gets large? Can the ratio be calculated without a computer?
    Mathematica gives that e/(a+b+c+d+e) is about 0.109 for n=20, FWIW.
     
    Last edited: Sep 28, 2011
  2. jcsd
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