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rN_t, & N_t < K

\end{cases}$

The steady states are when $N_{t + 1} = N_t = N_*$.

$$

N_{*} =\begin{cases}rN_*^{1 - b}, & N_* > K\\

rN_*, & N_* < K

\end{cases}

$$

So the steady states are $N_* = \sqrt

**{r}$ and $N_* = 0$.**

I am not sure how to check for stability and bifurcations values for a piece wise defined model.

I am not sure how to check for stability and bifurcations values for a piece wise defined model.