What is a Sequential Dynamical System?

The purpose of this chapter is to give an idea of what sequential dynamical systems (SDS)1 are and discuss the intuition and rationale behind their structure without going into too many technical details. The reader wishing to skip this chapter may proceed directly to Chapter 4 and refer to background terminology and concepts from Chapter 3 as needed. The structure of SDS is influenced by features that are characteristic of computer simulation systems and general dynamical processes over graphs. To make this more clear we have included short descriptions of some of the systems that motivated the structure of SDS. Specifically, we will discuss aspects of the TRANSIMS urban traffic simulation system, transport computations over irregular grids, and optimal scheduling on parallel computing architectures. Each of these areas is a large topic in itself, so we have necessarily taken a few shortcuts and made some simplifications. We have chosen to focus on the aspects of these systems that apply to SDS.