The effect of control strength on the synchronization in pinning control questions

This paper investigates the effects of control strength on nonlinearly coupled systems in the process of synchronization, where the coupling strength is an invariable constant. Under the assumption of an asymmetric and reducible coupling matrix, two comparable sufficient conditions are obtained by using the Lyapunov direct method. Moreover, a rough bound for the control strength is presented. A simple simulation is also given to show the validity of the theorems. This work improves the current results that we have.