Complex hybrid projective synchronization of complex-variable dynamical networks via open-plus-closed-loop control

In this paper, as a generalization of hybrid projective synchronization (HPS) in real-variable dynamical networks, complex hybrid projective synchronization (CHPS) in complex-variable dynamical networks is introduced and investigated using open-plus-closed-loop control. That is, the projective factors corresponding to complex-variable components are complex numbers. Both feedback control and intermittent control schemes are adopted to design closed loop controllers. Further, an adaptive strategy is introduced to design adaptive feedback controllers, where some constants with respect to system parameters including node dynamics and coupling matrices need not be calculated beforehand. Based on the Lyapunov function method and mathematical analysis technique, several sufficient conditions for achieving synchronization are derived. The theoretical results are illustrated to be effective by several numerical examples.