Cluster synchronization in directed networks of non-identical systems with noises via random pinning control

This paper is concerned with the issue of mean square cluster synchronization in directed networks, which consist of non-identical nodes infected by communication noises. The pinning control method is employed in designing controllers for guaranteeing cluster synchronization, meanwhile, all the controllers are supposed to occur with different probabilities by introducing the Bernoulli stochastic variables. Based on the Lyapunov stability theory and the stochastic theory, the sufficient synchronization conditions are derived and proved theoretically, which are mainly for the controllers to be designed and the noise intensities. Finally, some numerical examples are presented to demonstrate the effectiveness of the results.