On cycles of a discrete periodic logistic equation

For the discrete logistic equation $x_{k+1}=x_k\exp(r_k(1-x_k))$, $k\in Z_+$, where $\{r_k\}$ is a positive $n$-periodic sequence, it is shown that, under the condition $\prod^{n-1}_{k=0}(1-r_k)>1$, the equation has at least two positive $n$-cycles distinct from the equilibrium. Examples are considered.