Adapting Chaos Theory for Undergraduate Electrical Engineers

Abstract

The study of chaos has long attracted the attention of engineering, mathematics, and science educators. Most, if not all, courses dedicated to chaos are graduate-level courses requiring a broad understanding of linear and nonlinear systems. The exception would be differential equations, where chaos may be discussed as an optional topic of discussion. We argue that chaos is an attractive field of study for undergraduates that can raise their interest in interdisciplinary topics if the material is adapted, building on previous knowledge of ordinary differential equations, linear algebra, and probability. We propose an approach that involves discussions of one-dimensional maps, the harmonic oscillator, the Van der Pol Oscillator, and the Lorenz oscillator as building blocks, with corresponding simulations and implementation using integrated circuits such as op-amps and analog multipliers. In addition to equilibrium points, limit cycles, eigenvalue analysis, and feedback control, we introduce concepts such as bifurcation, phase-plane analysis, anti-control, and Lyapunov functions and exponents as discussions evolve. The course ends with a discussion of the synchronization of chaotic oscillators in the context of communications and radar applications. As designed, the course can become a senior technical elective that builds on junior-level electronics and signals and systems courses. Higher-level learning outcomes are analysis in the cognitive domain, the mechanism in the psychomotor domain, and value in the affective domain.