Complex Systems Modeling

This paper addresses the simulation of the dynamics of complex systems by using hierarchical graph and multi-agent system. A complex system is composed of numerous interacting parts that can be described recursively. First we summarize the hierarchical aspect of the complex system. We then present a de- scription of hierarchical graph as a data structure for structural modeling in parallel with dynamics simulation by agents. This method can be used by physiological modelers, ecological model- ers, etc as well as in other domains that are considered as complex systems. An example issued from physiology will illustrate this approach. Index Terms—Complex system, hierarchical graph, multi-agent system, modeling and simulation A system is considered as complex when a large number of elements, arranged in hierarchical structures are involved and, more important, when the interactions take place between ele- ments belonging to different levels (hierarchy, space, time) of the organization. For example, information paths and neurons in the nervous system have each multiple inner levels that we can model while keeping in sight the interactions between the different levels. The interactions between numerous parts of the system produce a emergent behavior that is difficult to predict from the collection of elementary specifications. To model this type of system, we have to take into account not only individ- ual entities features, but also interactions among components of different levels that happened in a real system. Traditional modeling and simulation methods offer just the vision of macro level behaviours, they do not provide insight views of micro level. Agent-based modeling appears as a suitable tool for sim- ulating complex systems behaviour, in which several thousand of interacting entities can reproduce the real system properties. Modelers can then observe, analyze and study the evolution of particular components and the emergence of collective be- haviour of the system under study. In this paper we will study the use of hierarchical graphs for modeling complex systems. More precisely, we will develop the theoretical aspects related to these modeling problems; in particular we will try to solve the questions related to the map- ping of these hierarchical graphs with the structural organiza- tion of the represented systems on one hand and its dynamics on the other hand. The paper is organized as follows. Section 1 is dedicated to a short presentation of a complex system, its properties and the need of simulation in order to observe the evolution of its be- haviour when facing to environmental changes. In section 2, the use of hierarchical graph in modeling the structural organi-