Rich-and-Poor Model for Human and Nature Interaction

Historical evidence shows collapse of several civilizations in different regions of the world. Jared Diamond presents an account of such societal failures in his 2005 book "Collapse: How Societies Choose to Fail or Succeed." As a precursor to building a complex model for interaction of human and environment, we developed a "thought-experiment" model based on Lotka-Volterra equations for the interaction of two species, known as the Predator-Prey model. We constructed a fairly simple rich-and-poor model that includes only four state variables (or stocks): Rich Population, Poor Population, Nature, and Rich Savings. We observed several scenarios for growth of societies by varying the model's parameter values, including scenarios that resemble the catastrophic fall of ancient civilizations such as the Maya and Anasazi.