Archetypes of Nonlinear Dynamics as Platforms for Undergraduate Research and Innovation

We have crafted an approach to fostering original research by undergraduates by identifying dynamical systems for which fundamental first-principle models and closely-connected experiments can spin off projects in which there is considerable room for novel and creative achievement. We call these systems “archetypes”. Even though many have been studied for decades, the spin-offs are far from being work that has already been done. Example systems and their fundamental dynamics include Hopf-bifurcation in the Wien-bridge oscillator, chaos in a parametrically forced pendulum, instability and pattern formation in flow between rotating cylinders (the Taylor-Couette system), and Hamiltonian dynamics associated with wave propagation in spatially-periodic optics. In addition to finding new theoretical, computational and experimental directions, a key goal has been to explore extensions into practical applications. We have also worked in the opposite direction, taking important applications like biomedicine and electric machinery and searching for underlying fundamental models that student can explore and expand.