Synchronization in complex network system with uncertainty

In this paper, we study the problem of synchronization in a network of nonlinear systems with scalar dynamics. The nonlinear systems are connected over linear network with stochastic uncertainty in their interactions. We provide a sufficient condition for the synchronization of such network system expressed in terms of the parameters of the nonlinear scalar dynamics, the second and largest eigenvalues of the mean interconnection Laplacian, and the variance of the stochastic uncertainty. The provided sufficient condition is independent of network size thereby making it attractive for verification of synchronization in a large size network. The main contribution of this paper is to provide analytical characterization for the interplay of role played by the internal dynamics of the nonlinear systems, network topology, and uncertainty statistics for the network synchronization. We show that there exist important trade-offs between these various network parameters necessary to achieve synchronization. We provide simulation results in network system with internal dynamics modeling of agents moving in a double well potential function. The synchronization of network happens whereby the dynamics of the network system flip from one potential well to another at the backdrop of stochastic interaction uncertainty.