The existence of generalized synchronization of chaotic systems in complex networks

The paper studies the existence of generalized synchronization in complex networks, which consist of chaotic systems. When a part of modified nodes are chaotic, and the others have asymptotically stable equilibriums or orbital asymptotically stable periodic solutions, under certain conditions, the existence of generalized synchronization can be turned to the problem of contractive fixed point in the family of Lipschitz functions. In addition, theoretical proofs are proposed to the exponential attractive property of generalized synchronization manifold. Numerical simulations validate the theory.