The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified response system collapses to an asymptotically stable equilibrium or asymptotically stable periodic orbit, under certain conditions, the existence of the generalized synchronization can be converted to the problem of a Lipschitz contractive fixed point or Schauder fixed point. Moreover, the exponential attractive property of generalized synchronization manifold is strictly proved. In addition, numerical simulations demonstrate the correctness of the present theory. The physical background and meaning of the results obtained in this paper are also discussed.
In this paper, the generalized synchronization of two unidirectionally coupled Ginzburg Landau equations is studied theoretically. It is demonstrated that the drive-response system has bounded attraction domain and compact attractors. It is derived that the correction equation has asymptotically stable zero solutions under certain conditions and that the sufficient conditions for smooth generalized synchronization and Holder continuous generalized synchronization exist in the coupling system. Numerical result analysis shows the correctness of theory.
