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- #1

by the difference equation

$$

u_{t+1}=\frac{au_t^2}{b^2+u_t^2}, \quad a>0.

$$

Determine the equilibria and show that if $a^2 > 4b^2$ it is possible for the populationto be driven to extinction if it becomes less than a critical size which you should find.

So the steady states are

$u_*=0$

$u_*=\frac{a\pm\sqrt{a^2-4b^2}}{2}$

So why if the solution is real, does the population go to extinction?