Robust network synchronization of time-delayed coupled systems

We address the problem of controlled synchronization in networks of time-delayed coupled nonlinear systems. In particular, we prove that, under some mild conditions, there always exists a unimodal region in the parameter space (coupling strength γ versus time-delay τ), such that if γ and τ belong to this region, the systems synchronize. We show how this unimodal region scales with the network topology, which, in turn, provides useful insights of how to design the network topology to maximize robustness against time-delays. The results are illustrated by computer simulations of coupled Hindmarsh-Rose neural chaotic oscillators.