Synchronized chaotic oscillations

When two or more chaotic systems are coupled they may exhibit synchronized chaotic oscillations. The synchronization of chaos is usually understood as the regime of chaotic oscillations in which the corresponding variables of coupled systems are equal to each other. This kind of synchronized chaos is most frequently observed in systems specifically designed to be able to produce this behavior.; In this dissertation a wider framework for synchronization of chaos is proposed. This framework is based on the concept of generalized synchronization of chaos. When coupled systems are synchronized in the generalized sense their corresponding variable are not simply proportional to each other, but connected by a certain transformation. The observations of this kind of synchronization in experiments with nonlinear electronic circuits indicate that this behavior can be observed in a wider variety of systems and therefore may play a more important role in nature than the identical synchronization of chaos. A part of this dissertation is dedicated to the study of this phenomenon.; The issue of robustness of synchronized chaotic oscillations with respect to noise and parameters variations is addressed. A criterion of robustness of synchronized chaos is suggested. It is shown that the loss of robustness occurs through bifurcations of saddle limit sets in the neighborhood of the chaotic set of synchronized oscillations. This analysis was done for the case of identical synchronized chaotic oscillations, however it is likely to be true in the case of generalized synchronization as well.; The possibility of achieving the identical synchronization of multiple chaotic systems coupled over a single channel is important for applications of chaos synchronization in communications. The consideration of this problem presented here demonstrates the principal possibility of such synchronization and uncovers a few practical limitations.; The synchronization of chaos is possible in spatially extended systems as well as in spatially localized system. A part of this dissertation illustrates that chaotic fields produced by coupled complex Ginzburg-Landau equations can be synchronized by a linear dissipative coupling.