What is a dynamical system and what is an evolution equation?
The term dynamical system implies that something is changing over time. That is what a dynamical system is: it is a system that changes over time. Typically, we will measure something about that system, giving us a series of data values from different timepoints.
Wait – isn’t this just time-series data that we met in Chapter 6? No – there is a difference here. When looking at time-series data, we have a series of data values, but we typically don’t consider the underlying system that generated that data. We only consider the relationships between data values at different timepoints, such as any auto-regressive structure present. In contrast, when studying dynamical systems, it is the underlying system we are interested in modeling.
The most important thing dynamical systems have is state. The state of a dynamical system is a variable or attribute, or a collection of variables or attributes...
