Consider the following difference equation for populations called the nonlinear logistic model
?t+1=?xt(1−xt)
(a) Find the equilibria. Here ?>0 is an unknown parameter (i.e., is a constant).
(b) Determine the values of r for which each equilibrium is stable.
so solution is
And so
We have as it is stable and
Which is so we must have
So stability criteria are
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