Working in Dr. Cressman’s lab has given me the opportunity
to continue my research on non-linear dynamical systems. I initially became
interested in Chua’s circuit as a sophomore while I was a lab assistant at the
Krasnow Institute, where I produced simulations of the circuit. During the fall
semester of my junior year, our focus was studying the fluctuation relation, a
non-equilibrium theory, in the context of Chua’s circuit. With funding from the
URSP, I have continued studying this system over the summer. Currently, we are exploring
different methods of perturbing the circuit to transition across different
stable states.
Unlike many-dimensional dynamical systems, Chua’s circuit is
a simple chaotic circuit that only requires a few electronic components, thus
making it easier to study in the lab. Chua’s circuit also has multiple
simultaneous stable states, and can transition from one state to another. Our
goal is to minimize the resources needed to move between states. We are
exploring the different methods of transitioning by applying small
perturbations of current in the circuit.
My work involves three main tasks: perturbing the circuit,
perturbing the model, and comparing data from both the circuit and the model. I
am also collaborating with professors from the mathematics department and using
algorithms to predict and calculate stable and unstable directions in the
system. One of the tools we use is called a Kalman filter, which is a
predicting algorithm that helps us to forecast the system in real time.
Additionally, we use the Kalman filter to verify and improve our model. The
experiments we conduct in the model are replicated in the physical system. Data
from both the model and circuit are then analyzed. From this data, we can
improve on our approach to perturb the system.
In the future, I would like to pursue a master’s degree in
engineering and focus on research. This project has given me a glimpse of what
that entails. I believe that I have learned some skills, in the lab, that will help
me with future academic and career goals. Above all, I have realized that
scientific results come from hard work and persistence. I am grateful for the
opportunity to contribute to science through my own work.
