Where cultures meet, there is bound to be conflict to some extent. This especially applies in the case of refugees grouped together when seeking asylum, with different styles of life, socialization, and conflict resolution meeting in one place. This paper focuses specially on three types of conflict resolution(negotiation, mediation, and arbitration) and constructs a differential equation model to study how the interactions between populations cause the number of people following each resolution method to shift. It was found that when there is no existing outside authority or environmental bias towards a resolution method, the method with the greatest number of followers will also be the one to take over the final population. However, in the presence of an outside force promoting or discouraging certain methods, although some groups will be given advantages over others, the final outcome is also still partially under the influence of the initial population. Outside of stable equilibria representing situations where one method ends up taking over the entire population, we also found certain unstable equilibria that carry key information about the basins of attraction of the stable equilibria.

Author Bio

Raaghav Malik is a high school junior at the Columbus Academy. He enjoys mathematics, physics, and computer science, and in his free time, loves playing the flute and tutoring. After participating in the SCUDEM challenge, his understanding of the applicable side of mathematics has vastly increased, and he has also improved in mathematical programming.

Alice Xu is a junior at Seven Lakes High School with an interest in mathematics and computer science. In her free time, she plays violin, runs school clubs, and volunteers in education organizations. The experience of the SCUDEM challenge increased her interest in the applicability of computer science to mathematics as well as the realistic applications of the topic.

Ruoxian is a junior student at Eastside Catholic School with a concentration in bioinformatics and biology. Besides academic study, she enjoys dancing and oil painting. The SCUDEM program helped Huang deepen her interest in math and develop collaboration skills.