Adaptive pinning synchronization on nonlinearly coupled complex networks with an asymmetrical matrix

In this paper, the global synchronization problem for a kind of complex dynamical networks with nonlinearly coupled functions and an asymmetrical coupling matrix is investigated by using pinning control. By designing the adaptive updating laws for the pinning feedback controller, some proper feedback control gains will be acquired. According to the Lyapunov stability theorem and the projection method, sufficient conditions are obtained that ensure the realisation of the global synchronization for the complex dynamical network with different initial values. Finally, the theoretical results are illustrated by a numerical experiment.