Series Editor:
Albert Luo, Ph.D., Southern Illinois University, Department of Mechanical and Industrial Engineering, Edwardsville, USA
George Zaslavsky, New York University, Courant Institute of Mathematical Sciences and Department of Physics, USA
By
Stefano Boccaletti, CNR-Istituto dei Sistemi Complessi, Sesto Fiorentino, Florence, Italy
Description
The origin of the word synchronization is a greek root, meaning "to share the common time". The original meaning of synchronization has
been maintained up to now in the colloquial use of this word, as agreement or correlation in time of different processes. Historically,
the analysis of synchronization phenomena in the evolution of dynamical systems has been a subject of active investigation since the
earlier days of physics.
Recently, the search for synchronization has moved to chaotic systems. In this latter framework, the appearance
of collective (synchronized) dynamics is, in general, not trivial. Indeed, a dynamical system is called chaotic whenever its evolution
sensitively depends on the initial conditions. The above said implies that two trajectories emerging from two different closeby initial
conditions separate exponentially in the course of the time. As a result, chaotic systems intrinsically defy synchronization, because
even two identical systems starting from slightly different initial conditions would evolve in time in a unsynchronized manner (the differences
in the systems' states would grow exponentially). This is a relevant practical problem, insofar as experimental initial conditions are
never known perfectly. The setting of some collective (synchronized) behavior in coupled chaotic systems has therefore a great importance
and interest.
The subject of the present book is to summarize the recent discoveries involving the study of synchronization in coupled
chaotic systems.
Not always the word synchronization is taken as having the same colloquial meaning, and one needs to specify what synchrony
means in all particular contexts in which we will describe its emergence.
The book describes the complete synchronization phenomenon,
both for low and for high dimensional situations, and illustrates possible applications in the field of communicating with chaos.
Furthermore,
the book summarizes the concepts of phase synchronization, lag synchronization, imperfect phase synchronization, and generalized synchronization,
describing a general transition scenario between a hierarchy of different types of synchronization for chaotic oscillators.
These
concepts are extended to the case of structurally different systems, of uncoupled systems subjected to a common external source, of space
extended nonlinearly evolving fields, and of dynamical units networking via a complex wiring of connections, giving thus a summary of
all possible situations that are encountered in real life and in technology.
Included in series
Monograph Series on Nonlinear Science and Complexity
Audience:
Senior graduate students, Established researchers in the area
