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.