FUNDAMENTALS OF SYNCHRONIZATION IN CHAOTIC SYSTEMS, CONCEPTS, AND APPLICATIONS

The field of chaotic synchronization has grown considerably since its advent in 1990. Several subdisciplines and ''cottage industries'' have emerged that have taken on boon fide lives of their own. Our purpose in this paper is to collect results From these various areas in a revi ew article format with a tutorial emphasis. Fundamentals of chaotic sy nchronization are reviewed first with emphases an the geometry of sync hronization and stability criteria. Several widely used coupling confi gurations are examined and, when available, experimental demonstration s of their :success (generally with chaotic circuit systems) are descr ibed. Particular focus is given to the recent notion of synchronous su bstitution-a method to synchronize chaotic systems using a larger clas s of scalar chaotic coupling signals than previously thought possible, Connections between this technique and well-known control theory resu lts are also outlined, Extensions of the technique are presented that allow so-called. hyperchaotic systems (systems with more than one posi tive Lyapunov exponent) to be synchronized. Several proposals for ''se cure'' communication schemes have been advanced: major ones are review ed and their strengths and weaknesses are touched upon. Arrays of coup led chaotic systems have received a great deal of attention lately and have spawned a host of interesting and, in some cases, counterintuiti ve phenomena including bursting above synchronization thresholds, dest abilizing transitions as coupling increases (short-wavelength bifurcat ions), and riddled basins. Ln addition, a general mathematical framewo rk for analyzing the stability of arrays with arbitrary coupling confi gurations is outlined. Finally, the topic of generalized synchronizati on is discussed, along with data analysis techniques that can be used to decide whether two systems satisfy the mathematical requirements of generalized synchronization. (C) 1997 American Institute of Physics.