Methods for Analytical Understanding of Agent-Based Modeling of Complex   Systems
  Von Neuman's work on universal machines and the hardware development have allowed the simulation of dynamical systems through a large set of interacting agents. This is a bottom-up approach which tries to derive global properties of a complex system through local interaction rules and agent behaviour. Traditionally, such systems are modeled and simulated through top-down methods based on differential equations. Agent-Based Modeling has the advantage of simplicity and low computational cost. However, unlike differential equations, there is no standard way to express agent behaviour. Besides, it is not clear how to analytically predict the results obtained by the simulation. In this paper we survey some of these methods. For expressing agent behaviour formal methods, like Stochastic Process Algebras have been used. Such approach is useful if the global properties of interest can be expressed as a function of stochastic time series. However, if space variables must be considered, we shall change the focus. In this case, multiscale techniques, based on Chapman-Enskog expansion, was used to establish the connection between the microscopic dynamics and the macroscopic observables. Also, we use data mining techniques,like Principal Component Analysis (PCA), to study agent systems like Cellular Automata. With the help of these tools we will discuss a simple society model, a Lattice Gas Automaton for fluid modeling, and knowledge discovery in CA databases. Besides, we show the capabilities of the NetLogo, a software for agent simulation of complex system and show our experience about. 
Gilson A. Giraldi, Luis C. da Costa, Adilson V. Xavier, Paulo S.   Rodrigues