  We study synchronisation properties of networks of coupled dynamical systems
with interaction akin to diffusion. We assume that the isolated node dynamics
possesses a forward invariant set on which it has a bounded Jacobian, then we
characterise a class of coupling functions that allows for uniformly stable
synchronisation in connected complex networks --- in the sense that there is an
open neighbourhood of the initial conditions that is uniformly attracted
towards synchronisation. Moreover, this stable synchronisation persists under
perturbations to non-identical node dynamics. We illustrate the theory with
numerical examples and conclude with a discussion on embedding these results in
a more general framework of spectral dichotomies.
