  An integrable system of two-component nonlinear Ablowitz-Ladik (AL) equations
is used to construct complex rogue-wave (RW) solutions in an explicit form.
First, the modulational instability of continuous waves is studied in the
system. Then, new higher-order discrete two-component RW solutions of the
system are found by means of a newly derived discrete version of a generalized
Darboux transformation. Finally, perturbed evolution of these RW states is
explored in terms of systematic simulations, which demonstrates that tightly
and loosely bound RWs are, respectively, nearly stable and strongly unstable
solutions.
