Pinning synchronization of complex dynamical networks with multiweights

In this paper, we introduce two complex dynamical networks with multiweights, which have several different sorts of weights between two nodes. By means of Lyapunov functional method and pinning control technique, some sufficient conditions are derived to ensure the synchronization for proposed network models. Moreover, some adaptive strategies are given to acquire suitable coupling strengths and feedback gains. By exploiting these designed adaptive laws, several general criteria for network synchronization are established. Finally, two numerical examples are also provided to show the validity of the theoretical results.