Department of Computer Science, University of Colorado, Boulder, Colorado 80304, USA.
Chaos. 2009 Sep;19(3):033124. doi: 10.1063/1.3187791.
In this paper, we propose a nonlinear dynamics-based framework for modeling and analyzing computer systems. Working with this framework, we use a custom measurement infrastructure and delay-coordinate embedding to study the dynamics of these complex nonlinear systems. We find strong indications, from multiple corroborating methods, of low-dimensional dynamics in the performance of a simple program running on a popular Intel computer-including the first experimental evidence of chaotic dynamics in real computer hardware. We also find that the dynamics change completely when we run the same program on a different type of Intel computer, or when that program is changed slightly. This not only validates our framework; it also raises important issues about computer analysis and design. These engineered systems have grown so complex as to defy the analysis tools that are typically used by their designers: tools that assume linearity and stochasticity and essentially ignore dynamics. The ideas and methods developed by the nonlinear dynamics community, applied and interpreted in the context of the framework proposed here, are a much better way to study, understand, and design modern computer systems.
在本文中，我们提出了一个基于非线性动力学的框架，用于对计算机系统进行建模和分析。在这个框架的基础上，我们使用定制的测量基础设施和延迟坐标嵌入来研究这些复杂非线性系统的动态。我们从多种相互印证的方法中找到了有力的证据，表明在一个流行的英特尔计算机上运行的一个简单程序的性能具有低维动力学——包括在真实计算机硬件中首次发现混沌动力学的实验证据。我们还发现，当我们在不同类型的英特尔计算机上运行相同的程序，或者当程序略有更改时，动力学会完全改变。这不仅验证了我们的框架；它还提出了关于计算机分析和设计的重要问题。这些工程系统变得如此复杂，以至于其设计者通常使用的线性和随机性分析工具已无法应对：这些工具本质上忽略了动力学。非线性动力学社区开发的思想和方法，在本文提出的框架中得到应用和解释，是研究、理解和设计现代计算机系统的更好方法。
