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stability
2001 Aug 10
1
An applied math question with solve()
...wth 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 by:
a[1,1] + a[1,2] + a[1,3] = 0
a[2,2] + a[2,1] + a[2,3] = 0
a[3,3] + a[3,1] + a[3,2] = 0
#se...