Sequential dynamical systems

Abstract

We present our work on the special class of dynamical systems referred to as discrete sequential dynamical systems (SDS). The definition of these systems is motivated by the generic structure of computer simulations. In computer simulations, we typically find agents or entities with certain properties or states. The entities can retrieve information from other entities, but usually only from the ones in their own vicinity. Based on these states, they may update their own state. A schedule will take care of the update order of the entities. One possible interpretation of this is to have each entity as a vertex in a (dependency) graph where two vertices are connected if the corresponding two entities can communicate. Without loss of generality, we can associate a binary state to each vertex or entity. Finally, we fix some ordering of the vertices that represents the update ordering of the entities. The above construction will be put in a strict mathematical context, and leads to the concept of a sequential dynamical system (SDS).