Generalized Synchronization in Spatially Extended Systems

We study the synchronization of a coupled pair of one-dimensional Kuramoto-Sivashinsky systems, generalized in different ways. It was found that with two different values of a parameter that characterizes the system synchronization exists in a generalized sense. It persists even in the extreme case when one of the equations is missing one derivative term. Master-slave synchronization error is small, so the generalized synchronization relationship is useful for predicting the state of the master from that of the slave. This result possibly could be extended for rather complex systems like the climate, where the role of the slave can be even a combination of simple models. The individual models comprising that combination also generally synchronize with each other.