Mathematical Modeling of Social Phenomena

Dr. Courtney Brown

Assignment #10

Using Phaser, you are to experiment with the predator-prey equations of Lotka and Volterra. You are to add limitations to their growth and understand why this means that each population is competing with its own members. You are to construct phase portraits that demonstrate all that you discover. In words (accompanying the plots), explain all that you have discovered, and answer the following questions. What form of the model will give you an attractor? What form of the model will give you periodic orbits (i.e., closed trajectories)? Can you find a basin? If so, where is it? Approximately where is the zero vector? Is this zero vector a likely equilibrium point? Why or why not? Construct a directional field portrait (sometimes called a vector field) for both forms of the model (i.e., with and without the growth limitations). Finally, construct time series plots to corroborate what is going on with the phase diagrams. Hand it all in.