Abstract

Network automata and the functional dynamic network framework

We introduce and define Network Automata, a generalization of Cellular Automata, which relates the topological evolution of a network to its structure. This framework is capable of replicating many familiar network models. We also introduce the Functional Dynamic Network framework for dealing with networks in which the topology evolves according to some specified microscopic rules and, simultaneously, there is a dynamic process taking place on the network that both depends on its structure but is also capable of modifying it. As such it is a generic framework for dealing with the types of systems in which network structure, dynamics, and function are interrelated. At the practical level, these frameworks allow for easy implementation of the microscopic rules involved in such systems. To demonstrate the Functional Dynamic Network in action, we develop a class of simple biologically inspired models of fungal growth.