Dynamical Systems

In this chapter, we introduce the concept of modeling a dynamic system – a system that changes over time according to some mathematical law. Why is that useful? Many systems we encounter in real-world data science are dynamical systems. They output data, and to understand that data we need to understand the underlying system. If we have a mathematical understanding of the underlying dynamical system, we can also use data from that system to make inferences and predictions about how the system will behave in the future – one of the key goals of doing useful data science.

This chapter will take a deliberate data science perspective on dynamical systems. Many traditional applied math books on dynamical systems will explain concepts such as phase plane diagrams, fixed points, basins of attraction, bifurcation points, and deterministic chaos. While highly relevant for dynamical systems and extremely interesting, we don’t have space to cover such...