Hybrid function projective synchronization in discrete dynamical networks via adaptive control

In this paper, we study the hybrid function projective synchronization between coupled complex discrete networks with different dimensions. The hybrid function projective synchronization is achieved by designing an adaptive control method. Based on the designed controller and the Lyapunov stability theory, we derive sufficient conditions to realize the hybrid function projective synchronization with different nodes. Moreover, with the adaptive update law, an adaptive control gains are obtained. Furthermore, we examine different cases of outer coupling matrix of node dynamics. Finally, we provide numerical examples to show the effectiveness of the proposed control scheme.