Colorado State University   Joint Applied Math / Applied Dynamics Lab Seminar

Applied Nonlinear Dynamics: Unusual Behavior in Self-Sustained Electronic Oscillators

By  Randy Tagg

CU Denver

When  Tuesday, April 24, 2018
3:00 pm
Where  Weber 201

One of the killer apps of nonlinear dynamics must surely be the electronic oscillator. We have explored both models and physical realizations of the Wien bridge oscillator, which is easy to build using a simple integrated circuit operational amplifier and a few extra components. Relatively few standard electronics textbooks describe such circuits in terms of limit cycle dynamics and yet this is a rich desktop example of many features and even some surprises in nonlinear systems modeling. One key surprise was a mode of oscillation in which the system settled into repeated bursting of cycles - a phenomenon called squegging in electronics literature - instead of settling into regular oscillation. Eliminating this behavior was a subtle issue regarding the choice of passive components used in the circuit. Once this possibly useful aberration was removed, we found that a common model for long-term behavior - the van der Pol equation - is more appropriately replaced with a model whose nonlinear term reflects the dissipated power. A prediction clearly borne out by experiment (which we will demonstrate using an actual circuit) is that the oscillator is very cleanly sinusoidal over a surprising range of amplitudes. Research extensions using this circuit as a building block include investigation of noise and fluctuations in the neighborhood of birfurcations and methods for coupling several oscillators together to form potentially useful networks such as central pattern generators for adaptive robotics. This then falls into a larger context in which we aim to discover practical uses for nonlinear dynamics in several sectors of what we call our Nonlinear PIE (Nonlinear Physics, Innovation, and Entrepreneurship).

Gerhard Dangelmayr, Iuliana Oprea, Patrick Shipman, David Aristoff