The geometry of chaos synchronization
The geometry of chaos synchronization
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作者：
Barreto, E;Josic, K;So, P
耦合系统中的混沌同步通常以组件状态之间的映射 phi 为特征。在不可逆系统中，或者在没有固有对称性的系统中，同步集（我们指的是图（phi））可能非常复杂。我们识别、描述并给出可能出现的几种不同复杂情况的示例，并将每个复杂情况与潜在动态的固有属性联系起来。简而言之，同步集通常可以变得不可微，并且在不可逆动力学的更严重的情况下，它们甚至可能是多值的。我们提出了两种不同的方法来量化这些特征，并且我们讨论了当这些特征存在时使用标准的基于连续性的方法检测混沌同步可能失败的情况。 (C) 2003 年美国物理研究所。
Chaos synchronization in coupled systems is often characterized by a map phi between the states of the components. In noninvertible systems, or in systems without inherent symmetries, the synchronization set-by which we mean graph(phi)-can be extremely complicated. We identify, describe, and give examples of several different complications that can arise, and we link each to inherent properties of the underlying dynamics. In brief, synchronization sets can in general become nondifferentiable, and in the more severe case of noninvertible dynamics, they might even be multivalued. We suggest two different ways to quantify these features, and we discuss possible failures in detecting chaos synchrony using standard continuity-based methods when these features are present. (C) 2003 American Institute of Physics.