The population of a certain species subjected to a specific kind of predation is modelled by the difference equation

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

Determine the equilibria and show that if $a^{2}>4 b^{2}$ it is possible for the population to be driven to extinction if it becomes less than a critical size which you should find. Explain your reasoning by means of a cobweb diagram.