Disk Graph-Based Model: A Graph Theoretical Approach for Linking Agent-Based Models and Dynamical Systems

In this work, we use disk graph theory to build a model called disk graph-based model (DGBM) for a case study in theoretical population ecology. The model, on one hand, represents behaviors of individuals of species as a given agent-based model (ABM). On the other hand, we prove that under some conditions the evolutionary equations of the total individuals of species in the model are the same as those of densities of species in a given dynamical system (DS) which is mostly represented by differential equations.