Implementation of non-linear oscillators using analog computers for the study of chaotic oscillators
Benjamin C. Flores, Hector Erives · 2024
Over the past decade, we have offered a course dedicated to the study of chaotic signals and systems.The course attracts senior and graduate students with an interest in hands-on projects.In the past, as part of the course, these students have implemented non-linear differential equations for harmonic, relaxation, and chaotic oscillators using dual-in-line packaged analog ICs.Typical breadboard electronic troubleshooting often challenges some students' psychomotor skills and confuses their learning experience, especially when the oscillator performance is already nonlinear and dependent on passive parameter tolerances and IC parameters.To mitigate some of these challenges, we propose the use of a hand-held analog computer as a clean alternative for implementing second/third-order, non-linear differential equations.The use of an analog computer simplifies the implementation of an oscillator design, relying on simple connections of adder, multiplier, inverter, and amplifier blocks, and enhances the student implementation experience.In this talk, we demonstrate the ease of implementation of the harmonic, Van de Pol (relaxation), Lorenz, and Rössler oscillators.Furthermore, we explore their behavior in the time domain, frequency domain, and state space.We will also discuss the assessment of psychomotor learning considering three basic levels of performance: perceiving, preparing, and responding to guidance.Relevant assessment rubrics are under development.