Stochastic synchronisation of nonlinear networks with additive measurement noise

Stochastic synchronisation of complex networks has recently attracted considerable attention because of the ubiquitousness of random noise in real-world complex systems. Previous works have mainly considered noise-corrupted communication by ignoring intrinsic dynamics of nodes. This work provides a systematic study of complex networks by taking into account both additive noise and nonlinear dynamics of nodes, examining their stochastic synchronisation problems. We model the deterministic diffusive coupling and noisy additive coupling with the time-invariant strength and the time-varying strength, respectively. Using the stochastic Lyapunov technique, this framework enables an analytical treatment of the problem, ultimately leading to sufficient conditions for the onset of synchronisation. For symmetrical/asymmetrical connections, the synchronisation condition for the time-invariant coupling strength can be stated elegantly in terms of node dynamics and network topology, whereas that for the time-varying coupling strength is described as a robust condition. Finally, two simulation examples are carried out to illustrate the effectiveness of theoretical findings.