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Insurgencies and occupiers model

  1. Mar 19, 2012 #1
    so the model where i(t) = insurgencies and o(t) = occupiers
    i' = o(α - Fi),
    o' = βi + (C - ρo)

    its from this website http://www.idea.wsu.edu/Insurgency/
    I tried solving it and
    I did find the first excercise which was easy enough

    so
    for
    1) eq. points
    this is what i found
    [ (α/F), (βα/Fρ) + C/ρ ]
    [ (-C/β), 0 ]

    2) it ask me to linearize so i did the jacobian and using the eq points
    i found the iegenvalues
    λ = (βα/ρ + FC/ρ + ρ) /2 +- √((βα/ρ + FC/ρ + ρ) 2 - 4 (αβ + FC)
    λ = -ρ/2 +- √(ρ2 + 4 (αβ + FC)

    3-4) it ask me how F will affect the model if F < 0 , F = 0 , and F > 0
    so i played around with the graph on the website but I couldnt really figure out
    what kind of a graph is it
    will F be saddle at F =0 and F>0
    is there a sink? somewhere

    oh I also need to find C
    but I dont know how
    any help would be appreciated


    tnx...
     
  2. jcsd
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