14 November 2011
My project will examine predator-prey equations and experiment with them using the exercises on pages 150-151 of the PyOpenGL notes by Stan Blank to lead to a better understanding of the equations, what they model, and how sensitive they are to change. I will look specifically at the Lotka-Volterra equations and define terms that apply to the topic.
I started with research into predator-prey equations and dynamical systems in general to gain a better understanding of what exactly they are modeling. Also, I have experimented with the first three of Stan Blank’s exercises. As my computer refused to correctly perform the random function, I could not complete the fourth exercise. However, you deemed it unnecessary to attempt to fix this, as this particular exercise has little merit or bearing on the project as a whole.
In my research, I came across a program in WolframAlpha that graphed predator-prey equations. I used it in the presentation, and you suggested I look into it further to determine exactly what it shows. While a predator-prey equation should have only one distinct cycle when graphed parametrically, this grapher showed many solutions. This brought up the question as to whether it was showing only the given initial conditions or all initial conditions.