Adaptive pinning synchronization of a general complex dynamical network

This paper further investigates and answers two fundamental questions in the complex dynamical networks: i) how many nodes should a general complex dynamical network with fixed network structure and coupling strength be pinned to reach network synchronization? ii) how much coupling strength should a general complex dynamical network with fixed network structure and pinning nodes be employed to reach network synchronization? In the above framework, the coupling-configuration matrix and the inner-coupling matrix are not necessarily symmetric. Also, the pinning nodes can be randomly selected. Furthermore, our adaptive pinning controllers are rather simple compared with some traditional controllers. Finally, a BA network example is then given to show the effectiveness of the proposed synchronization criteria.