Positive role of multiplication noise in attaining complete synchronization on large complex networks of dynamical systems

•The dynamical networks with complex structure are investigated.•The condition of synchronization is acquired by theoretical analyses.•Theoretical result shows noise plays a positive role in attaining synchronization.•The key role of eigenvalues of coupling matrix in attaining synchronization is revealed. In this paper, the role of multiplicative noise in attaining complete synchronization on large complex networks of dynamical systems is investigated by theoretical analysis and numerical simulations. Based on the stability theory of stochastic differential equation, we prove that the multiplicative noise plays a positive role in attaining synchronization if the complex networks of dynamical systems are bounded. Moreover, the theoretical result shows that smaller second eigenvalue of coupling matrix is of benefit in attaining complete synchronization. To demonstrate the correctness of theoretical results, the coupled Lorenz systems, Hindmarsh–Rose neuronal systems and Rössler-like systems are performed as numerical examples.