Tutorial and tests

This work has been supported by the project CARESSE (MISTIC-UJF pole).

A dynamical system is a fixed rule that describes what future  states follow from the current state. Its evolution is described by a fixed phase space and it is supported by a static graph. But in many applications, including communication networks, embedded systems or biological behaviors (such as collaboration or communication between ants, behavior of a set of cells which share local information, etc.) graphs are subject to discrete changes, such as additions or deletions of agents or links. In the last decade there has been a growing interest in such dynamically changing graphs. The difficulty of such structures is to deal, simultaneously, with the evolution of a number of agents (or nodes), the number of links between agents, the states of agents, and eventually, the states of links.
For biological problems, specific particular models have been developed such as L-systems, adaptive dynamics, TreeGCS (hierarchical Growing Cell Structures) and DS2 (Dynamical System with a Dynamic Structure) . On the other hand, for robotic problems, graph grammar theory has been used.
In this software, we propose a framework called Dynamical system based on dynamic graphs such that agents and links
between agents corespond, respectivly, to nodes and edges of a graph.

- Each node of the graph obeys a dynamical system,
- Each edge of the graph obeys a dynamical system,
- The evolution of nodes and edges is determined thanks to the state of there neighborhood.
- Under specific conditions, the graph evolves thanks to transformation rules.

Nodes and edges can be added to or removed from the graph. The graph evolution is determined thanks to local transformation rules. Our aim is to model agent reactions due to local informations. Consequently, transformation rules are function of a node and its neighborhood, or, of an edge and its neighborhood. We have implemented the framework of Dynamical system based on dynamic graphs in a program called DynSys. In the following parts, we will present this software:

- the first part is devoted to the configuration of Dynsys.
- the second part explains how to create a dynamical system
- the third part presents some examples
- the last part explains how to install the software and how to install it on various platforms (linux,windows)