  In this manuscript, we study the problem of robust synchronization in
networks of diffusively time-delayed coupled nonlinear systems. In particular,
we prove that, under some mild conditions on the input-output dynamics of the
systems and the network topology, there always exists a unimodal region in the
parameter space (coupling strength versus time-delay), such that if they belong
to this region, the systems synchronize. Moreover, we show how this unimodal
region scales with the network topology, which, in turn, provides useful
insights on how to design the network topology to maximize robustness against
time-delays. The results are illustrated by extensive simulation experiments of
time-delayed coupled Hindmarsh-Rose neural chaotic oscillators.
