Group synchronization in complex dynamical networks with different types of oscillators and adaptive coupling schemes

This paper focus on schemes and corresponding criteria for group synchronization in complex dynamical networks consisted of different group of chaotic oscillators. The global asymptotically stable criteria for a linearly or adaptively coupled network are derived to ensure each group of oscillators synchronize to the same behavior. Theoretical analysis and numerical simulation results show that the group synchronization can be guaranteed by enhancing the external coupling strength whenever there are connections or not within the groups under the “same input” condition. All of the results are proved rigorously. Finally, a network with three groups, a scale-free sub-network, a small-world sub-network and a ring sub-network, is illustrated, and the corresponding numerical simulations verify the theoretical analysis.