Abstract for:Approximating Network Dynamics in the Classic Maya Collapse
Using system dynamics to model history is useful for testing historical hypotheses. As an introduction of system dynamics modeling into Cliodynamics (mathematical modeling of history), we use the collapse of the Classic Maya. Lowe (1985) proposed a three-state system to model the warfare component of the Classic Maya collapse. He assumed the Classic Maya formed a system of independent city-states, where each city-state was either marginally stable, in crisis mode, or collapsed. His differential equations for this model are similar to the mean-field SIR model and include terms representing fighting between stable and crisis sites, fighting among crisis sites (called backwash), and an external pressure term. In this paper, we reproduce Lowe’s model using system dynamics, and we also provide a network version of the model where each site can interact with an average number of contacts. To approximate network dynamics, we use a pair-wise modeling approach, which is typically used to model the spread of infectious diseases and is new to system dynamics modeling. We show that the network dynamics model without the backwash and external pressure terms provides a better fit to the reference data than Lowe’s mean-field model.