Question

Consider the following difference equation for populations called the nonlinear logistic model ?t+1=?xt(1−xt) (a) Find the...

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.

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Answer #1

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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