Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems.
TL;DR: Necessary and sufficient conditions for the occurrence of generalized synchronization of unidirectionally coupled dynamical systems are given in terms of asymptotic stability and the existence of generalized synchronized systems in the case of parameter mismatch between coupled systems leads to a new interpretation of recent experimental results.
Abstract: Necessary and sufficient conditions for the occurrence of generalized synchronization of unidirectionally coupled dynamical systems are given in terms of asymptotic stability The relation between generalized synchronization, predictability, and equivalence of dynamical systems is discussed All theoretical results are illustrated by analytical and numerical examples In particular, the existence of generalized synchronization in the case of parameter mismatch between coupled systems leads to a new interpretation of recent experimental results Furthermore, the possible application of generalized synchronization for attractor reconstruction in nonlinear time series analysis is discussed
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TL;DR: Results from various areas of chaotic synchronization are collected in a review article format with a tutorial emphasis, with particular focus on the recent notion of synchronous substitution-a method to synchronize chaotic systems using a larger class of scalar chaotic coupling signals than previously thought possible.
Abstract: The field of chaotic synchronization has grown considerably since its advent in 1990. Several subdisciplines and “cottage industries” have emerged that have taken on bona fide lives of their own. Our purpose in this paper is to collect results from these various areas in a review article format with a tutorial emphasis. Fundamentals of chaotic synchronization are reviewed first with emphases on the geometry of synchronization and stability criteria. Several widely used coupling configurations are examined and, when available, experimental demonstrations of their success (generally with chaotic circuit systems) are described. Particular focus is given to the recent notion of synchronous substitution—a method to synchronize chaotic systems using a larger class of scalar chaotic coupling signals than previously thought possible. Connections between this technique and well-known control theory results are also outlined. Extensions of the technique are presented that allow so-called hyperchaotic systems (syste...
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