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equilibrium
2001 Aug 10
1
An applied math question with solve()
...estion.
I want to find equilibrium population density values for a system of linear
population growth equations (e.g., Pimm and Lawton 1977). The eventual goal
is to
perform stability analysis. I can find the partial differential equations
for the Jacobian matrix, but I get stuck trying finding the equilibriuym pop
densities (X*). Here is the (incorrect?) R code for for the X*:
# An attempt at stabiltiy analysis.
# Each pop growth equation - (Not code) is dXi/dt = Xi ( bi +
Sum(a[i,j]Xj) )
# Set dX/dt = 0, divide both sides by Xi and you get bi + sum(aijXj) = 0
# For three species this is represented b...