Deriving difference equation describing agent-based models

Abstract

Agent-based approaches are increasingly gaining popularity in modeling physical systems. However, understanding its inner workings is intrinsically difficult. We start here by finding the corresponding difference equation for a given simple agent-based (AB) model without the use of complicated mathematical derivations. The dynamics of the corresponding difference equation is shown similar to that of the derived from simple local rules in the AB model. Starting point for finding the set of rules that will generate system dynamics similar to the logistic equation (and other difference equations) is recommended.