The dynamics of predators and prey

Summary

This project results in a Lotka-Volterra model which simulates the dynamics of the predator-prey relationship. The model is first applied to a system with two-dimensions, but is then extended to include more complicated scenarios.

Learning Goals

Mathematical skills:
Graphing and interpreting graphs in phase space
Changing parameters to change the solution shape

Technical skills:
Writing functions which take in and return vectors

Communications skills:
Presenting their work as a mathematical result while also providing context to understand solution to the corresponding real-life problem.

Context for Use

This project works as a final project in a course with undergraduate students who have taken calculus. Before attempting this project, students should be able to write functions as .m files and should be able to plot in Matlab. Mathematically, they should understand the structure of vectors and should be familiar with Euler's method (or another method) to solve a dynamical system. The students work in groups of 3 or 4 (an appropriate class size is around 15).

Description and Teaching Materials

To complete this project, students should have access to MATLAB (or other simulation software).
Prior to this lab, students should have discussed Euler's method for approximating the solutions to differential equations. They should have created a MATLAB function which runs Euler's method.
This is a self-guided research project, so various sources are suggested. Several of these sources offer particular parameter values to represent different situation, so that students can explore the varied dynamics achieved by a two-dimensional Lotka-Volterra model.
Finally, students consider the Lotka-Volterra model as it applies to epidemiology (with a specific 'disease' of zombie-ism). This advances the model to higher dimensions.
Student Handout for Predator-Prey Modeling (Acrobat (PDF) 37kB Oct2 17)

Teaching Notes and Tips

Students have needed guidance in extending their one-dimensional Euler Method to higher dimensions.

Assessment

Students include their codes, which should perform their intended purposes. Students present their conclusions, which take the form of graphs and the oral descriptions of the graphs. Effectively, they are asked to 'tell a story' using their graph as supporting evidence.