How to determine bifurcation diagram for following system of difference equations?

Question

So given this system, $\begin{gather*}N_{t+2}=N_t\exp[r(1-\frac{N_t}{K})]\frac{1-e^{-aP_t}}{aP_t}\\ P_{t+1}=N_t[1-\frac{1-e^{-aP_t}}{aP_t}]\end{gather*}$, how do I determine the bifurcation diagram? The varying parameter is $a$, and trying to determine an explicit form of $N$ and $P$ in terms of $a$ has turned out to be fruitless. If anyone has any pointers or know of any matlab recipe that can do it, please comment below