I would like some help in investigating the stablity of the difference equation $$ \begin{cases} x_{n+1}=b x_n e^{ay_n} \\ y_{n+1}=b x_n (1-e^{-ay_n}) \end{cases} $$ at (0,0).
I know that if b<1, then the variational matrix at (0,0) has 1 eigenvalue b,and in this case there is asymptotical stability. but I do not know how to determine the stability in other cases. thx in advance.