Shil'nikov's theorem-a tutorial
Shil'nikov's theorem-a tutorial
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DOI：
10.1109/81.246142
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发表时间：
1993-10
影响因子：
5.1
通讯作者：
C. P. Silva
中科院分区：
文献类型：
--
作者：
C. P. Silva
在实验和计算机模拟环境中，混沌现象已经在许多非线性确定性系统中被观察到。然而，鉴于这种现象的性质，需要一种分析工具来确保所观察到的不是用于测量或模拟给定系统的设备的工件。本文提供了一个教程，介绍这些工具中为数不多但最有用的一个：Shil'nikov定理及其各种扩展。本文介绍了与Shil'nikov结果相关的基本术语和概念，对其用于3D系统的两个基本版本的正式陈述和后续讨论，以及Shil'nikov方法在分段线性系统中的两个示例应用。>
The phenomenon of chaos has been observed in many nonlinear deterministic systems in both experimental and computer-simulation contexts. Given the nature of this phenomenon, however, an analytical tool is needed to ensure that what is observed is not an artifact of the device used to measure or simulate the given system. This paper provides a tutorial look at one of the few and most useful of such tools: Shil'nikov's theorem and its various extensions. This exposition presents the basic terminology and concepts related to Shil'nikov's results, a formal statement and subsequent discussion of its two basic versions for 3D systems, as well as two example applications of Shil'nikov's method to a piecewise-linear system. >