Building a Better Cat

This chapter opens with a discussion of the idea of scientific modeling, showing some different types of scientific models and discussing the utility of such models. After considering some simple example models from physics and genetics, we propose developing a model of the predation of rabbits by foxes. We first explore how the rabbit population will grow exponentially in the absence of foxes (and given unlimited grass to eat). Discrete and continuous time models of population growth are considered. The death of foxes in the absence rabbits is also modeled. Once a full two-equation predator–prey differential equation model has been developed, we solve it numerically, finding that in most cases the number of foxes and rabbits oscillates. The special case of a steady-state solution is also considered. We next nondimensionalize the model to remove some of the nuisance parameters. After exploring the phase-plane representation of the system, we extend it to three species/dimensions and discover cases where chaotic behavior is seen.