This talk will describe an interesting generalization of the famous logistic equation from population dynamics. The logistic equation assumes that the environment's carrying capacity is a constant. We generalize this scenario to allow for periodic fluctuations in the environment's carrying capacity. This provides an elementary model of seasonal changes in the environment. Some interesting results include: (1) solutions to the model must be obtained using numerical approximations, as standard solution methods cannot provide exact formulas for solutions; (2) solutions with differing initial populations converge to a single, periodic solution; (3) the model may provide some insight into real population dynamics in biology.
