Pecora Louis M., Carroll Thomas L., Johnson Gregg A., Mar Douglas J., Heagy James F.
Code 6343, U.S. Naval Research Laboratory, Washington, District of Columbia 20375.
Chaos. 1997 Dec;7(4):520-543. doi: 10.1063/1.166278.
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 (systems with more than one positive Lyapunov exponent) to be synchronized. Several proposals for "secure" communication schemes have been advanced; major ones are reviewed and their strengths and weaknesses are touched upon. Arrays of coupled chaotic systems have received a great deal of attention lately and have spawned a host of interesting and, in some cases, counterintuitive phenomena including bursting above synchronization thresholds, destabilizing transitions as coupling increases (short-wavelength bifurcations), and riddled basins. In addition, a general mathematical framework for analyzing the stability of arrays with arbitrary coupling configurations is outlined. Finally, the topic of generalized synchronization 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.
自1990年混沌同步领域出现以来，它已取得了显著发展。多个子学科和“小型产业”纷纷涌现，并拥有了各自独立的发展态势。本文的目的是以综述文章的形式收集这些不同领域的研究成果，并着重进行教程式讲解。首先回顾混沌同步的基本原理，重点在于同步的几何结构和稳定性判据。研究了几种广泛使用的耦合配置，并在可行的情况下描述了它们成功的实验演示（通常是针对混沌电路系统）。特别关注同步替代这一最新概念——一种使用比之前认为可能的更大类标量混沌耦合信号来同步混沌系统的方法。还概述了该技术与著名控制理论结果之间的联系。提出了该技术的扩展，使得所谓的超混沌系统（具有多个正李雅普诺夫指数的系统）能够实现同步。已经提出了几种“安全”通信方案；对主要方案进行了综述，并探讨了它们的优缺点。耦合混沌系统阵列最近受到了广泛关注，并产生了许多有趣的、在某些情况下甚至违反直觉的现象，包括在同步阈值之上的突发、随着耦合增加而出现的失稳转变（短波分岔）以及满布吸引子盆地。此外，概述了一个用于分析具有任意耦合配置的阵列稳定性的通用数学框架。最后，讨论了广义同步的主题，以及可用于判定两个系统是否满足广义同步数学要求的数据分析技术。（c）1997美国物理学会。
