Introduction: Control and synchronization in chaotic dynamical systems.

exopl athe unof me ics r nd ired n a its onby esobded rian n tal of a The last ten years have seen remarkable developmen the research of chaotic dynamics, particularly with respec the interaction of chaotic dynamics with other fields of r search and with applications. There is now a developed ence of chaos that has as an essential underpinning the s interaction of theory and experiment. This is a depart from earlier times in which theoretical work existed large in the absence of substantial experimental realizations. Al with this new orientation has come increased apprecia and concern for the implications of chaotic dynamics in pr tical applications. Issues in topics such as the active con of chaotic systems in a broad variety of situations, the us chaos for communication, and the synchronization of cha dynamics for various purposes, are at the forefront of rec application topics in nonlinear science. The common thr through those topics is the marriage between knowledg the basic mathematical properties of chaos and specific p tical considerations of various applications. This Focus Issue resulted from a six-week event at Max Planck Institute for Physics of Complex Systems Dresden in the Fall of 2001. During that Worshop/Semin especially interesting and challenging topics on control a synchronization were addressed. We believe that success the research work coming out from that program will ha far-reaching technological and economical impact for broad area of important practical systems ranging from sers, via engineering to neuroscience and medicine. This issue focuses onControl and Synchronization in Chaotic Dynamical Systems . The fundamentals and the ma jor concepts involved in this area were reviewed in Chaosin a Focus Issue in December 1997 @Chaos7 ~4!#. Since that time, the then novel topics and applications have matu making this area well-established within nonlinear scien Elements and concepts from the theory of systems con and the theory of communication have been brought in, g ing the whole topic a firmer foundation. Therefore, the p