Abstract: My project will examine predator-prey equations and experiment with them using the five 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.
The project will include a brief explantation of chaos and dynamical systems, also covering terms you mentioned, like the difference between smooth and discrete dynamical systems.
So far, I've done some research into the Lotka-Volterra equations using the PyOpenGL notes, Wolfram, http://math.fullerton.edu/mathews/n2003/lotka-volterramod.html, and the book I borrowed: Introduction to Differential Equations.
The equations are differential equations that relate the population growth rates of two species: a predator and its prey. The growth rates of each species depend on the current populations of both. In addition, it cycles over time. The initial populations and four positive constants determine the behavior of the system, and there is one point at which the system has equilibrium.