The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with it various kinds of chaotic phases. Which are then the possible types of time delays, induced chaotic states, and methods suitable to characterize the resulting dynamics? This review presents an overview of the field that includes an in-depth discussion of the most important results, of the standard numerical approaches and of several novel tests for identifying chaos. Special emphasis is placed on a structured representation that is straightforward to follow. Several educational examples are included in addition as entry points to the rapidly developing field of time delay systems.

中文翻译：

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时间延迟系统中的混沌，教育评论

当各个系统通过微分方程建模时，在物理世界中交换信息所需的时间会导致延迟项。因此，时间延迟无处不在，还可能导致不稳定性以及随之而来的各种混乱阶段。那么，哪些可能的时间延迟类型、诱发的混沌状态和适合表征结果动力学的方法是什么？本综述对该领域进行了概述，其中包括对最重要的结果、标准数值方法和几种用于识别混沌的新测试的深入讨论。特别强调易于遵循的结构化表示。此外，还包括几个教育示例，作为进入快速发展的时间延迟系统领域的切入点。