Graphical interface as a teaching aid for nonlinear dynamical systems

Abstract

Chaos theory is an important breakthrough in understanding nonlinear dynamical systems. It is generally accepted that chaotic systems involve transitivity, a high density of periodic points in metric space, and extreme sensitivity to changes in initial conditions. Many systems taught on undergraduate courses satisfy these conditions, such as electronic circuits or computer simulations of nonlinear dynamical systems. However, a good understanding of these concepts is broadly difficult to achieve on such courses, and especially so at the undergraduate level. In view of this, we have developed an interactive standalone graphical user interface, which is platform-independent. The interface didactically simulates six chaotic systems. It allows the user to study a particular system without prior knowledge of computer programming, demonstrating rich dynamical behaviour such as fixed points, periodic cycles and deterministic chaos. At the same time, the interface provides details of the simulation and the parameters used, as well as some of the leading references. We provide the complete code and a detailed installation guide, which should make it easy to use the interface reliably and with little overhead work. We also provide a comparison with other available software for reference, and as a guide to readers who would like to explore this fascinating subject in more depth or with alternative approaches. Lastly, we present the results of a survey of 30 students who used our graphical user interface, revealing that it is an easy-to-use tool in the process of learning about chaotic dynamical systems.