On synchronization in continuous-time networks of nonlinear nodes with state-dependent and degenerate noise diffusion

In this paper, we present a generalization of a recent result on the almost sure consensus for networks affected by relative-state-dependent measurement noise. Specifically, we give two sufficient conditions for the synchronization of networks of diffusively coupled nonlinear nodes affected by certain state-dependent noise diffusion processes. We use this condition to study the onset of synchronization in a network of Lorenz systems and collective opinion dynamics.