Introduction
The previous chapters dealt with classical approaches in data science: statistics, machine learning, and signal processing. In this chapter and the next chapter, we will cover a different type of approach. Instead of analyzing data directly, we will simulate mathematical models that represent how our data was generated. A representative model gives us an explanation of the real-world processes underlying our data.
Specifically, we will cover a few examples of dynamical systems. These mathematical equations describe the evolution of quantities over time and space. They can represent a wide variety of real-world phenomena in physics, chemistry, biology, economics, social sciences, computer science, engineering, and other disciplines.
In this chapter, we will consider deterministic dynamical systems. This term is used in contrast to stochastic systems, which incorporate randomness in their rules. We will cover stochastic systems in the next chapter.
Types of dynamical systems
The...
