This invaluable book studies synchronization of coupled chaotic circuits and systems, as well as its applications. It shows how one can use stability results in nonlinear control to derive synchronization criteria for coupled chaotic circuits and systems. It also discusses the use of Lyapunov exponents in deriving synchronization criteria. Both the case of two coupled systems and the case of arbitrarily coupled arrays of systems are considered. The book examines how synchronization properties in arrays of coupled systems are dependent on graph-theoretical properties of the underlying coupling topology. Finally, it studies some applications of synchronized chaotic circuits and systems, including spread spectrum and secure communications, coupled map lattices and graph coloring.

Contents:

• Synchronization in Two Coupled Chaotic Systems
• Synchronization in Coupled Arrays of Chaotic Systems
• Synchronization in Coupled Arrays: Dynamic Coupling
• Graph Topology and Synchronization
• Lyapunov Exponents Approach to Synchronization
• Appendices:
• Some Linear Systems Theory and Matrix Theory
• Graph-Theoretical Definitions and Notations
• Stability, Lyapunov's Direct Method and Lyapunov Exponents
• Chaotic Circuits and Systems

"Wu's book presents a very readable introduction to the synchronization of chaos and its application in circuits ... the book is mathematically oriented and adequately formal for anyone who is interested in getting a good background in this area."

"The book may be useful for students and researchers interested in the synchronization theory as well as for those who are interested in practical designing of coupled chaotic circuits."