|InterJournal Complex Systems, 1727
|Manuscript Number: |
Submission Date: 2006
|Modelling complex systems by integration of agent-based and dynamical systems methods|
Existing models for complex systems are often based on quantitative, numerical methods such as Dynamical Systems Theory, and more in particular, differential equations. Such approaches often use numerical variables to describe global aspects of the system and how they affect each other over time; for example, how the number of predators affects the number of preys. An advantage of such numerical approaches is that numerical approximation methods and software environments are available for simulation. The relatively new agent-based modelling approaches to complex systems take into account the local perspective of a possibly large number of separate agents and their specific behaviours in a system; for example, the different individual predator agents and prey agents. These approaches are usually based on qualitative, logical languages. An advantage of such logical approaches is that they allow (automated) logical analysis of the relationships between different parts of a model, for example interlevel relationships between global properties of the (multi-agent) system as a whole and local properties of the basic mechanisms within (agents of) the system. Complex systems, for example organisms in biology or organisations in the socio-economic area, often involve both qualitative aspects and quantitative aspects. It is not easy to cover both types of aspects in one modelling method. One the one hand, it is difficult to incorporate logical aspects in differential equations. For example, qualitative behaviour of an agent that depends on whether the value of a variable is below or above a threshold is difficult to describe by differential equations. On the other hand, quantitative methods based on differential equations are not usable in the context of most logical, agent-based modelling languages, as these languages are not able to handle real numbers and calculations. This paper shows an integrative approach to simulate and analyse complex systems, integrating quantitative, numerical and qualitative, logical aspects within one expressive temporal specification language. To obtain a simulation model, an executable sublanguage of this language is used to specify the complex systemís mechanisms in detail. It is shown how both the existing numerical methods for approximation and simulation (such as the Runge-Kutta methods) and the existing methods for logical analysis (such as the establishment of interlevel relationships between global dynamics and dynamics of basic mechanisms) can be used. Thus in this approach also an integration of modelling at the global level and modelling at a local level is made.
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