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System of difference equations with Mathematica

  1. May 16, 2012 #1
    Hello all,
    I am attempting to characterize a molecular pathway through a system of difference equations:

    W[n + 1] = W[n] - b*L[n]*W[n] + nw
    H[n + 1] = (1 - dwl)*H[n] + b*W[n]*L[n]
    G[n + 1] = G[n] - g*H[n] + ng
    B[n + 1] = (1 - t)*B[n] - e*G[n] + nb
    T[n + 1] = (1 - dd)*T[n] + t*B[n]
    L[n + 1] = L[n] + f*T[n] - b*L[n]*W[n]

    where b, nw, dwl, g, ng, t, e, nb, dd, and f are all constants.
    n refers to the iteration.

    I currently have two problems and would appreciate any input:

    1) RSolve in mathematica won't solve it as soon as I include the product of W[n] and L[n] in my system of equations. Does this make the system unsolvable fundamentally or unsolvable just for Mathematica?

    Below is the complete function call (I have solved a simpler system without the L[n]*W[n] this way):

    Clear["Global`*"];
    Clear[n];

    RSolve[
    {W[n + 1] == W[n] - b*L[n]*W[n] + nw,
    H[n + 1] == (1 - dwl)*H[n] + b*W[n]*L[n],
    G[n + 1] == G[n] - g*H[n] + ng,
    B[n + 1] == (1 - t)*B[n] - e*G[n] + nb,
    T[n + 1] == (1 - dd)*T[n] + t*B[n],
    L[n + 1] == L[n] + f*T[n] - b*L[n]*W[n],
    W[0] == 2, H[0] == 2, G[0] == 36, B[0] == 320, T[0] == 16, L[0] == 4},
    {W[n], H[n], G[n], B[n], T[n], L[n]}, n
    ]

    2) In general, not just for the system above, let's say that I want to simplify a system into a single higher order equation (e.g. W[n],W[n+1],W[n+2], etc.). Can this be done in Mathematica? My current websearch has not revealed any example.

    Thank you.
     
  2. jcsd
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