Exploring dynamical systems and chaos using the logistic map model of population change

Abstract

The logistic map difference equation is encountered in the theoretical ecology literature as a mathematical model of population change for organisms with non-overlapping generations and density-dependent dynamics influenced solely by intraspecific interactions. This article presents the logistic map as a simple model suitable for introducing students to the properties of dynamical systems including periodic orbits, bifurcations, and deterministic chaos. After a brief historical and mathematical introduction to models of population change and the logistic map, the article summarizes the logistic map activities I teach in my introductory physics laboratories for non-physics majors. The logistic map laboratory introduces the many bioscience students in my courses to a foundational model in population ecology that has inspired ecologists to recognize the importance of nonlinear dynamics in real populations. Although I use this activity in courses for non-majors, the logistic map model of population change could also be taught to physics majors to introduce properties of dynamical systems while demonstrating an application of mathematical modeling outside of traditional physics.