Adaptive hybrid synchronization of the complex dynamical network with non-derivative and derivative coupling

First of all, we impose matrix transform on the state vector of the master and slave systems, the master and slave systems could be synchronized under the transform, this case would be called hybrid synchronization in this paper. Secondly, we investigate adaptive hybrid synchronization of the complex dynamical network with non-derivative and derivative coupling. Based on Lasalle's invariance principle, adaptive synchronization criteria is obtained. Analytical result shows that the complex dynamical network with nonderivative and derivative coupling can asymptotically hybrid synchronize to a given trajectory under the designed adaptive controllers. What is more, the coupling matrix is not assumed to be symmetric or irreducible. Finally, simulations results show that the method proposed in this paper is effective.