Summary
This chapter has been about dynamical systems, but from a data science perspective. That means we have focused on those dynamical systems that are heavily used in data science modeling. Consequently, we have spent most of the chapter focusing on Markov chain models – first-order and higher-order discrete Markov processes. Despite the outward simplicity of discrete Markov models, they are a very powerful tool for modeling real-world scenarios. To help understand discrete Markov models, in this chapter, we have covered the main concepts underlying their behavior. Those concepts are the following:
- A dynamical system has a state, and that state changes over time.
- For some dynamical systems the time variable is continuous, while for other dynamical systems the time variable is discrete.
- An evolution equation determines how a dynamical system evolves.
- First-order discrete Markov processes are probabilistic discrete-time models that specify how a system...
