Projective synchronization between two delayed networks of different sizes with nonidentical nodes and unknown parameters

This paper investigates the projective synchronization between two delayed networks of different sizes with nonidentical nodes and unknown parameters. The two complex networks are of diverse dynamical nodes, different topological structures and different sizes. Both networks contain unknown parameters and coupling delay. Based on stability theory, the bidirectional coupling control condition is proposed to ensure the realization of projective synchronization between the two delayed networks. During synchronization, the unknown parameters are successful estimated by adaptive updated laws. Furthermore, in numerical simulations, the Small-World network and Scale-Free network based on well-known Lorenz system and Chen system are constructed. The results verified the effectiveness of the proposed synchronization method.