ABSTRACT
This chapter starts with the logistic map, a model for the variations in insect populations with time. This map and others are simple yet provide surprisingly complex behaviors, and are also appropriate as problems in Classical Dynamics. Biological populations often display complex dynamics that can be modeled rather simply. The chapter explores several models, starting with the most elementary and adding refinements, with even the simplest model capable of producing surprising complex and chaotic dynamics. The logistic map is simple, though maybe too much so to be a realistic model of population dynamics. The Lotka-Volterra Model (LVM) extends the logistic map to predator and prey populations coexisting in the same geographical region. The chapter presents three models for growth of plants and proteins. A protein is a large biological molecule containing chains of nonpolar hydrophobic monomers that are repelled by water and polar monomers that are attracted by water.
