Computer systems are dynamical systems

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.