Teaching Contemporary Mathematics Conference January 25, 2013 Christine Belledin NC School of Science and Mathematics

 Models where individuals in the environment are unique and autonomous  Individuals vary in certain characteristics such as  Location  Ability or skill level  Resource reserves  Individuals interact with each other and their environment  Agents have only local knowledge and interactions  Each agent pursues its own objectives  Agents use adaptive behavior – they adjust their behavior based on their current state, their neighboring agents, or their environment

 ABM’s can be used to study system dynamics that arise from the way that individual agents interact with each other and their environments  ABM’s are across-level models  Examples of questions ABM’s have been used to investigate  How can we manage tropical forests in a sustainable way?  How do shorebird populations respond to loss of the mudflats they feed in, and how can this be addressed in a cost-effective way?  What causes the complex and seemingly unpredictable dynamics of a stock market?  How should electricity grids be developed in developing countries?

 Based on work by Nobel laureate Thomas Schelling  Explores relationship between segregation patterns and tolerance of individuals for unlike neighbors

First consider the original model where birds change their heading based on multiple neighbors.

Now consider a new version of the model where birds change their heading based only on their nearest neighbor.

Shows distribution of wealth over time as measured graphically by a class histogram and numerically by the Gini IndexGini Index

Perfect equity: Gini Index = 0 Perfect inequity: Gini index = 1