Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Physics & Astronomy

First Advisor

Dani S. Bassett


Many systems of biological interest exhibit oscillatory behavior, from the beating of a heart to the firing of neurons to the flashing of fireflies. Further, these oscillatory agents are rarely isolated from one another, and so may interact with one another. In the presence of such interactions, one possible outcome is synchronization of the oscillatory motions. Such synchrony may be observed in the simultaneous flashing of a great many fireflies, or the simultaneous firing of many neurons during an epileptic seizure. A classic model that captures this synchronization is the Kuramoto model. However, the Kuramoto model is a toy model, and thus much work has been directed to extending the model by introducing additional dynamics. In the dissertation, we will present two extensions of the Kuramoto model that make it more appropriate to the study or neural systems. The first extension will add a resource dependence to the Kuramoto dynamics, making the internal dynamics of the oscillators more complex, and thereby introducing novel phases into the Kuramoto phase diagram (Chapter 2). The next extension will allow the oscillators to compete for a shared supply of resources, creating a secondary avenue of communication between the oscillators (Chapter 4). This additional communication pathway will generate correlations in behavior, which may have some relevance for the differences observed between functional and structural connectivity measures in the brain. These two studies serve to elucidate some interesting results on the dynamics of Kuramoto oscillators competing for shared resources, and so serve as my primary contribution to the study of the physics of synchronizable systems. Further, as a scientist-educator, I am also interested in and committed to the education of young physicists, and so I have pursued a separate line of inquiry that studies the learning of students in a cross-disciplinary network-neuroscience course using the tool of concept networks (Chapter 6). We will find that student-drawn concept networks are a useful tool in studying the learning process at a high level, but that more thought needs to be put toward optimizing the collection task in order to bring out the full power of this tool. Collectively, these three studies --- two in the physics of dynamical systems and one in education --- have enabled me to develop in my role as a scientist-educator.

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