so the model where i(t) = insurgencies and o(t) = occupiers(adsbygoogle = window.adsbygoogle || []).push({});

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...

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# Insurgencies and occupiers model

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