# Dr. Richard Cangelosi

### Applied Mathematics Student Research Group

Student Research Projects

Unraveling the Linx-Hare Paradox

Unraveling the Linx-Hare Paradox

- Kyle Black - Dual Mathematics and Economics Major
- Lydia Pane - Mathematics Major; Chemistry Minor
- Emilie Pratt - Biology Major

*. The Hudson Bay Company's pelt trading records of the Canadian lynx and snowshoe hare is possibly the best know data set in ecology. Over 100 years of data is available which dates back to the early 19th century. Using pelts as a proxy for the population density, textbooks on ecology or mathematical biology frequently present the Lotka-Volterra equations as a simple predator-prey model for this famous data set. The model exhibits limit cycle behavior; however, it suggests that hare eat lynx! Students working on this project are developing a mathematical population model to explain this apparent paradox. In addition to the lynx and hare populations, students will examine a model which includes a lower trophic level (vegetation) upon which the hare feed. A fourth predator population population, which preferentially targets the lynx, will also be considered.*

Project Description

Project Description

Chaos in an Economic Model for Duopoly Pricing

Chaos in an Economic Model for Duopoly Pricing

- Trent DeGiovanni - Dual Mathematics and Economics Major
- Joseph Kincanon - Economics Major; Mathematics Minor
- Elijah Michaelson - Computer Sciences Major

*Project Description*. T. Puu (1991) presents a discrete time model for a market dominated by two competing firms (a duopoly). The model assumes iso-elastic demand and constant unit production costs to determine each firm's production level. Students plan to investigate certain mathematical aspects of the Puu (1991) model as well as investigate extensions of the model.